bluuebunny/crossref_metadata_2025 huggingface dataset:
Solutions of Multiparameter Systems of Elliptic Differential Equations
Authors: Gawrycka Joanna , Rybicki Slawomir
Published: March 2016

In this article we study bifurcations of weak solutions of the following multiparameter variational system of elliptic differential equations:

We formulate necessary and sufficient conditions for the existence of bifurcation points and global bifurcation points of weak solutions of this system.
Unbounded Motions of Perturbed Isochronous Hamiltonian Systems at Resonance
Authors: Fabry Christian , Fonda Alessandro
Published: March 2016

Large amplitude solutions of asymptotically positively homogeneous perturbations of hamiltonians systems at resonance can be unbounded, either in the past, or in the future. We present conditions for boundedness or unboundedness, generalizing in particular the results obtained by Alonso and Ortega [1] for scalar second order equations with asymmetric nonlinearities.
Periodic Solutions for Delay Competition Systems and Delay Prey-Predator Systems
Authors: Bereanu Cristian
Published: March 2016

Using Mawhin’s continuation theorem, sufficient conditions are obtained for the existence of positive periodic solutions for periodic delay-Lotka-Volterra systems.
Locating the Peaks of Semilinear Elliptic Systems
Authors: Pomponio Alessio , Squassina Marco
Published: March 2016

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function Σ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of Σ in the sense of subdifferential calculus.
Variational Eigenvalues of Degenerate Eigenvalue Problems for the Weighted p-Laplacian
Authors: Lê An , Schmitt Klaus
Published: March 2016

We prove the existence of nondecreasing sequences of positive eigenvalues of the homogeneous degenerate quasilinear eigenvalue problem − div(a(x)|▽u|p-2▽u) = λb(x)|u|p-2u, λ > 0 subject to Dirichlet boundary conditions on a bounded domain . The diffusion coefficient a(x) is a function in L1
loc(Ω) and b(x) is a nontrivial function in Lr(Ω) (r depending on a, p and N) and may change sign. We use Ljusternik-Schnirelman theory, minimax theory and the theory of weighted Sobolev spaces to establish our results.
On the Prescribed Scalar and Zero Mean Curvature on 3-Dimensional Manifolds With Umbilic Boundary
Authors: Ahmedou Mohameden Ould
Published: March 2016

In this paper we consider the existence and the compactness of Riemannian metrics of prescribed mean curvature and zero boundary mean curvature on a three dimensional manifold with umbilic boundary (M, g0). We prove that for three dimensional manifolds with umbilic boundaries, which are not conformally equivalent to the three dimensional standard half sphere, any positive function can be realized as the scalar curvature of a Riemannian metric g conformal to g0 with respect to which the boundary has zero mean curvature. Moreover, all such metrics stay bounded with respect to the C2,α -topology and in the nondegerate case Morse inequalities hold.
Multiple Positive Solutions For a Class of Nonlinear Elliptic Equations
Authors: Weng Shenghua , Li Yongqing
Published: March 2016

This paper deals with a class of nonlinear elliptic Dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results.
The p-Laplace Heat Equation With a Source Term: Self-similar Solutions Revisited
Authors: Bidaut-Véron Marie Françoise
Published: March 2016

We study the self-similar solutions of any sign of the equation

ut - div(|▽u|p-2▽u) = |u|q-1u,

in ℝN, where p, q > 1. We extend the results of Haraux-Weissler obtained for p = 2 to the case q > p-1 > 0. In particular we study the existence of slow or fast decaying solutions. For given t > 0, the fast solutions u(t, .) have a compact support in ℝN when p > 2; and |x|p/(2-p) u(t, x) is bounded at infinity when p < 2: We describe the behaviour for large |x| of all the solutions. According to the position of q with respect to the first critical exponent p - 1 + p/N and the critical Sobolev exponent q*, we study the existence of positive solutions, or the number of the zeros of u(t, .). We prove that any solution u(t, .) is oscillatory when p < 2 and q is closed to 1.
Multiplicity of Solutions For a Convex-concave Problem With a Nonlinear Boundary Condition
Authors: Abreu Emerson A.M. , Carrião Paulo C. , Miyagaki Olímpio H.
Published: March 2016

We study the existence of multiple positive solutions for a convex-concave problem, denoted by (Pλμ), with a nonlinear boundary condition involving two critical exponents and two positive parameters λ and μ. We obtain a continuous strictly decreasing function f such that K1 ≡ {(f(μ), μ) : μ ∈ [0, ∞)} divides [0, ∞) × [0, ∞) \ {(0, 0)} in two connected sets K0 and K2 such that problem (Pλμ) has at least two solutions for (λ, μ) ∈ K2, at least one solution for (λ, μ) ∈ K1 and no solution for (λ, μ) ∈ K0.
Multiple Positive Solutions For Nonautonomous Quasicritical Elliptic Problems in Unbounded Domains
Authors: Cerami Giovanna , Molle Riccardo
Published: March 2016

The problem

with boundary Dirichlet zero data is considered in an exterior domain Ω ⊂ ℝN. Assuming that, as ε →0, aε concentrates and blows up at a point of Ω, namely

the existence of at least 2 distinct positive solutions is proved, if

is suitably small. Furthermore, if aε(x) has a suitable behaviour at infinity, the existence of another positive solution is shown.
On the Geodesic Connectedeness of a Class of Lorentzian Manifolds with Boundary
Authors: Masiello Antonio
Published: March 2016

In this paper we study the geodesic connectedeness of a class of Lorentzian manifolds with boundary, extending the result of [13]. The results are obtained using variational methods.
Uniqueness and Exact Multiplicity of Solutions For Non-autonomous Dirichlet Problems
Authors: Korman Philip
Published: March 2016

We consider positive solutions for a class of non-autonomous equations on a unit ball in Rn

Δu + f(|x|, u) = 0 for |x| < 1, u= 0 when |x| = 1.

We assume that fr(r, u) ≤ 0, so that in view of [8] all positive solutions are radially symmetric. If f(|x|, u) = a(|x|)g(u), we obtain several exact multiplicity results for a class of convex-concave g(u), with g(0) = 0. In another direction, we obtain uniqueness and non-degeneracy of positive solutions for a class of equations, modeled on f(|x|, u) = −a(|x|)u + b(|x|)up, with

.
Concentration Phenomena in a Biharmonic Equation Involving the Critical Sobolev Exponent
Authors: Selmi Abdelbaki
Published: March 2016

In this paper, we consider the problem

Δ2u = |u|8/(n-4)u + εf(x, u)

in Ω, u = Δu = 0 on ∂Ω, where Ω is a bounded and smooth domain in ℝn, n ≥ 6, ε is a small positive parameter, and f is a smooth function. Our main purpose is to construct families of solutions which concentrate around some well defined points depending on f.
Multiple Symmetric Brake Orbits in Bounded Convex Symmetric Domains
Authors: Zhang Duanzhi
Published: March 2016

In this paper, we prove that there exist at least two geometrically distinct symmetric brake orbits in every bounded convex symmetric domain in Rnfor n ≥ 2.
On the Fixed Homogeneous Circle Problem
Authors: Azevêdo C. , Ontaneda P. , Cabral H. E.
Published: March 2016

We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in the plane that contains the circle. The study presented here is purely analytic.
Existence and Concentration of Positive Solutions For Coupled Nonlinear Schrödinger Systems in ℝN
Authors: Wan Youyan
Published: March 2016

The aim of this paper is to study the existence and concentration of positive solutions for the coupled nonlinear Schrödinger system

where ε is a small positive number, N ≥ 3, p, q > 1 satisfy

and W(x), Q(x), K(x) are continuous and bounded positive functions defined in ℝN. Combining the dual variational methods with mountain pass theorem, we prove under some conditions on W, Q, K the existence of a family of positive solutions concentrating at a point where related functionals achieve their minimum energy.
Existence of Nonnegative Solutions For a Class of p-Laplacian Equations in IRN
Authors: Dai Shuang , Yang Jianfu
Published: March 2016

We consider the question of existence of nonnegative solutions of a class of p-Laplacian elliptic problems in the whole space ℝN having a sign-changing nonlinearity of the form a(x)g(u).
Nonexistence of Positive Solutions for Polyharmonic Systems in ℝN
Authors: Guo Yuxia , Liu Jiaquan , Zhang Yajing
Published: March 2016

This work is devoted to the nonexistence of positive solutions for polyharmonic systems

(−Δ)mu = f(u, v), (−Δ)mv = g(u, v).

Byusing the method of moving plane combined with integral inequalities and Hardy’s inequality, we prove some new Liouville type theorems for the above semilinear polyharmonic systems in ℝN.
On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in ℝN
Authors: Bellazzini J. , Ghimenti V. Benci M. , Micheletti A.M.
Published: March 2016

We study an eigenvalue problem for functions in ℝN and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear Schrödinger equation.
A Note on The Schrödinger-Poisson-Slater Equation on Bounded Domains
Authors: Ruiz David , Siciliano Gaetano
Published: March 2016

In this note we consider the problem

where u, ϕ ∈ H0
1(Ω) and Ω ⊂ ℝ3 is a smooth bounded domain. We are interested in

existence and multiplicity of solutions depending on the parameters p and λ. Our results extend previous work made in ℝ3.
Solitary Waves in Abelian Gauge Theories
Authors: Benci Vieri , Fortunato Donato
Published: March 2016

Abelian gauge theories consist of a class of field equations which provide a model for the interaction between matter and electromagnetic fields. In this paper we analyze the existence of solitary waves for these theories. We assume that the lower order term W is positive and we prove the existence of solitary waves if the coupling between matter and electromagnetic field is small. We point out that the positiveness assumption on W implies that the energy is positive: this fact makes these theories more suitable to model physical phenomena.
Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System
Authors: Gan Zaihui
Published: March 2016

This paper deals with the instability of the ground state solitary wave solution to the Klein-Gordon-Zakharov system in three space dimensions with c ≥ 1, which is a model to describe the Langmuir turbulence in plasma. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational calculus and scaling argument. Then by defining invariant sets and applying some priori estimates, we prove the orbital instability of the ground state in the following sense: in each neighborhood of it, there exists a solution whose energy diverges in finite or infinite time.
Critical Boundary Source Exponent in a Doubly Degenerate Parabolic Equation
Authors: Jiang Zhaoxin , Zheng Sining
Published: March 2016

This paper deals with a doubly degenerate parabolic equation with absorption (un)t = (|ux|m-1ux)x - ηup in (0, 1) × (0, T) subject to the boundary source (|ux|m-1ux)(1, t) = uq(1, t). The critical boundary source exponent qc is determined under different dominations to identify global and non-global solutions. A complete classification for all of the four nonlinear exponents m, n, p, q with the coefficient η draws a very clear picture of interactions among the multi-nonlinearities. It is shown that qc depends on the absorption exponent p if and only if p > n. It is found as well that qc is related to small m only: qc relies on m if and only if m < p when p > n, also qc relies on m if and only if m < n when p ≤ n. The behavior of solutions in the critical case of q = qc is interesting. The absorption coefficient η affects the critical property of solutions with q = qc if and only if p > n: the case q = qc belongs to the global existence situation (regardless of the absorption coefficient η) if p ≤ n; while for q = qc with p > n, the solutions may be both global and non-global, depending on the size of the absorption coefficient.
Hopf Bifurcation in Presence of 1 : 3 Resonance
Authors: Cima Anna , Libre Jaume , Teixeira Marco Antonioy
Published: March 2016

Assume that the linear part at a singular point p0 of a C4 differential system Y0 in ℝ4 has eigenvalues ±αi and ±βi such that β/α = 1/3. In the main result of the paper we exhibit a one-parameter family of systems Yε for ε ∈ (-δ0;+δ0) where is shown that the original vector field around p0 can bifurcate in 0, 1, 2, 3 or 4 one-parameter families of periodic orbits. The tool for proving such a result is the averaging theory for non-C1 differentiable system. Moreover, assuming now that Yε is a one-parameter family of ℤ2- reversible polynomial vector fields of degree 5, we show that it can bifurcate in 0 or 2 one-parameter families of periodic orbits.
Absence of Global Solutions to Systems of Perturbed Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term
Authors: Toscano Luisa
Published: March 2016

For a wide class of systems of nonlinear parabolic inequalities with Chipot-Weissler nonlinearity in the gradient term which depend on two nonnegative parameters λ1 and λ1, we study the nonexistence of global solutions according to the \test function" method. We establish theorems that, when λ1 = λ1 = 0, include and, in some cases, improve, or, in part, yield the results obtained by Es- cobedo and Herrero; Escobedo and Levine; Galaktionov;Levine, Lieberman and Meier; Mitidieri and Pohozaev; Pohozaev and Tesei.
Exponential Growth Rates of Periodic Asymmetric Oscillators
Authors: Zhang Meirong , Zhou Zhe
Published: March 2016

In this paper we will study the dynamics of the periodic asymmetric oscillator xʺ + q+(t)x+ + q–(t)x– = 0, where q+; q– ∊ L1(ℝ / 2πℤ) and x+ = max(x; 0), x– = min(x; 0) for x ∊ ℝ. It will be proved that the exponential growth rate

does exist for each non-zero solution x(t) of the oscillator. The properties of these rates, or the Lyapunov exponents, will be given using the induced circle di®eomorphism of the oscillator. The proof is extensively based on the Denjoy theorem in topological dynamics and the unique ergodicity theorem in ergodic theory.
Asymptotic Nondegeneracy of Least Energy Solutions to an Elliptic Problem with Critical Sobolev Exponent
Authors: Takahashi Futoshi
Published: March 2016

Consider the problem

-∆u = N(N - 2)up + εk(x)u in Ω, u > 0 in Ω, u|∂Ω = 0

where Ω­ is a smooth bounded domain in ℝN (N ≥ 6), p = (N +2)/(N - 2), ε > 0 and k ∈ C2(Ω̅). Under certain assumptions, we prove the nondegeneracy of least energy solutions to the above problem as Ɛ →0. This is an extension of the recent work of Grossi [9].
Moduli Space Theory of Constant Mean Curvature Hypersurfaces
Authors: Jleli Mohamed
Published: March 2016

In this paper, we study the set of complete noncompact hypersurfaces in ℝn+1 which have constant mean curvature equal to 1 and a finite number of ends. By means of the application of the implicit function theorem, we will prove that this set has a smooth structure near any nondegenerate element. We start by a review of the functional properties of elliptic operators acting on functions defined on a manifold with cylindrical ends. This will explain the central role played by the indicial roots about an n-Delaunay hypersurface. Then, we will explain how to apply the implicit function theorem in our setting. We partially generalize, in any dimension, the results of R. Kusner, R. Mazzeo and D. Pollack.
Comparison Principle For Quasilinear Parabolic Inclusions with Clarke’s Gradient
Authors: Carl Siegfried , Motreanu Dumitru
Published: March 2016

We prove existence and comparison results for quasilinear parabolic inclusions with Clarke’s generalized gradient via appropriately defined sub-supersolution only assuming a local Lq-boundedness condition on Clarke’s gradient. The developed comparison principle allows us to show the equivalence of the considered parabolic inclusion with an associated evolutionary hemivariational inequality.
A Note on Asymptotically Linear Schrödinger Equation on ℝN
Authors: Zhu Hongbo
Published: March 2016

This paper is concerned with the following nonlinear Schrödinger equation:

where

f(x, t)t-1 < μ* := inf σ(-Δ + V) <

f(x, t)t-1 < V(∞) =

V(x). The existence of a positive solution and a least energy solution for problem (P) are discussed. Here, we assume neither that f(x, t) ≡ f(t), nor that f(x, t)t-1 is non-decreasing on t ≥ 0. Furthermore, we do not require that f(x, t) have a limit as |x| → +∞.
Connected Branches of Initial Points for Asymptotic BVPs, With Application to Heteroclinic and Homoclinic Solutions
Authors: Margheri Alessandro , Rebelo Carlota , Zanoliny Fabio
Published: March 2016

We consider the second order nonlinear ODE uʺ – f(t, u) = 0 and assume that f(·, υ0) ≡ 0; for some υ0 ∈ ℝ. We prove the existence of closed connected sets Γ ⊆ ℝ2 of initial points such that for each (α, β) ∈ Γ there exists a solution u(·) of the given differential equation, with (u(t0), uʹ(t0)) = (α, β) and (u(t), uʹ(t)) → (υ0, 0) as t → –∞ (or as t → +∞). These results are then applied to the search of heteroclinic and homoclinic solutions.
Retarded Functional Differential Equations on Manifolds and Applications to Motion Problems for Forced Constrained Systems
Authors: Benevieri Pierluigi , Calamai Alessandro , Furi Massimo , Pera Maria Patrizia
Published: March 2016

We prove an existence result for T-periodic retarded functional differential equations of the type xʹ(t) = f(t, xt), where f is a T-periodic functional tangent vector field on a smooth manifold. As an application we show that any constrained system acted on by a periodic force, possibly with delay, admits a forced oscillation provided that the constraint is a topologically nontrivial compact manifold and the frictional coefficient is nonzero. We conjecture that the same assertion holds true even in the frictionless case.
Symmetry-Breaking for Immersed Constant Mean Curvature Hypersurfaces
Authors: Jleli Mohamed
Published: March 2016

In this paper we prove the existence of constant mean curvature hypersurfaces which are cylindrically bounded and which bifurcate from the family of immersed constant mean curvature hypersurface of revolution. Based on the study of the spectrum of the Jacobi operator (the linearized mean curvature) about this family, the existence of new branches follows from a bifurcation result of Crandall and Rabinowitz.
Brunn-Minkowski-Type Inequalities Related to the Monge-Ampère Equation
Authors: Hartenstine David
Published: March 2016

We prove Brunn-Minkowski-type inequalities for functionals related to nontrivial weak solutions of Dirichlet boundary value problems for Monge-Ampère equations of the form det D2u = |u|P, where 0 ≤ p < n, in bounded strictly convex domains in ℝn. The expected equality conditions are also established. These results generalize inequalities known for analogous problems for the p-Laplacian. The existence of solutions to these problems is an extension of known results for more regular domains, and is proved by approximation. The principal technique used in the proof of the main theorem is the same as that used to establish a similar inequality for the eigenvalue of the Monge-Ampère operator.
Existence and Regularity Results for Anisotropic Elliptic Problems
Authors: Di Castro Agnese
Published: March 2016

We study existence and regularity of the solutions for some anisotropic elliptic problems with homogeneous Dirichlet boundary conditions in bounded domains.
Topological Remarks–Critical Points at Infinity and String Theory
Authors: Bahri Abbas
Published: March 2016

We take the example of the standard geodesics problem on S2 to show how the point to circle Morse relations in the periodic orbits variational problem for contact vector-fields lead directly to the existence of critical points at infinity. This is sharply in contrast with the phenomena encountered in symplectic geometry where the variational problems are not necessarily S1-invariant and where the Hamiltonians are usually bounded. The related tools defined in this area do not exhibit therefore all the phenomena encountered in S1-invariant settings. We then recall our definition of Contact Form Homology which includes these essential Morse relations and we define related tools for its computation.
Positive Solutions for Elliptic Equations With Supercritical Nonlinearity
Authors: Rabelo Paulo
Published: March 2016

In this paper minimax methods are employed to establish the existence of a bounded positive solution for semilinear elliptic equation of the form

−∆u + V (x)u = P(x)|u|p−1u + Q(x)|u|q−1u in ℝN,

where the nonlinearity has supercritical growth and the potential can change sign. The solutions of the problem above are obtained by proving a priori estimates for solutions of a suitable auxiliary problem.
A Smooth Pseudo-Gradient for the Lagrangian Action Functional
Authors: Abbondandolo Alberto , Schwarzy Matthias
Published: March 2016

We study the action functional associated to a smooth Lagrangian function on the tangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable on the Hilbert manifold consisting of H1 curves, it is a Lyapunov function for some smooth Morse-Smale vector field, under the generic assumption that all the critical points are non-degenerate. This fact is suffcient to associate a Morse complex to the Lagrangian action functional.
On Some Nonhomogeneous Elliptic Problems in Unbounded Domains
Authors: Candela A.M. , Cerami G. , Palmieri G.
Published: March 2016

In this paper we consider the problem

where Ω = ℝN ∖ ω̅, ω being a nonempty open bounded domain of ℝN having smooth boundary

We prove that, if u0 and f are nonnegative and satisfy suitable conditions, there exist at least two positive solutions. Moreover, the existence of a solution is shown to hold even when no condition on the sign of u0 and f is assumed.
Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values
Authors: Dancer E.N.
Published: March 2016

We consider weakly nonlinear elliptic equations with small diffusion in the case where the nonlinearity has a non-nodal zero. We show that there is an unexpected connection with problems with infinite boundary values.
An Alternative Variational Principle for Geodesics of a Randers Metric
Authors: Masiello Antonio
Published: March 2016

We present an alternative variational principle for the geodesics of a Randers metric. We define a functional I on the manifold of H1,2 curves joining two points on a Randers manifold (M, F) defined by a Riemannian metric g and a differential form ω. The functional I is of class C2, so it is more regular than the usual action functional, which is only of class C1,1. Moreover the critical points of the functional I are the geodesics for the Randers metric F reparameterized with Riemannian length g constant. Some global properties of the functional I are investigated. Finally some applications to the Fermat principle in stationary spacetimes will be presented.
Existence of 2–Nodal Solutions for Semilinear Elliptic Equations in Unbounded Domains
Authors: Li Tiexiang , Lin Huei-li , Wu Tsung-fang
Published: March 2016

In this paper, we study the effect of domain shape on the existence of 2-nodal solutions for a semilinear elliptic equation involving non-odd nonlinearities.
Multiple Nontrivial Solutions for Neumann Problems Involving the p-Laplacian: a Morse Theoretical Approach
Authors: Kristály Alexandru , Papageorgiou Nikolaos S.
Published: March 2016

We consider nonlinear elliptic Neumann problems driven by the p-Laplacian. Using variational techniques together with Morse theory (in particular, critical groups and the Poincaré-Hopf formula), we prove some multiplicity results: either three or four distinct nontrivial solutions are guaranteed, depending on the geometry and smoothness of the nonlinear term.
Existence and Blow-up Results for Fast Diffusion Equations with Nonlinear Sources
Authors: Giachetti Daniela , Porzio Maria Michaela
Published: March 2016

In this paper we prove existence and blow-up results for a class of filtration equations in presence of suitable reaction terms. In particular we cover the case of principal part of fast diffusion type.
An Asymptotical Stability in Variational Sense for Second Order Systems
Authors: Idczak Dariusz , Walczak Stanisław
Published: March 2016

In this paper, a new, variational concept of asymptotical stability of zero solution to an ordinary differential system of the second order, considered in Sobolev space, is presented. Sufficient conditions for an asymptotical stability in a variational sense with respect to initial condition and functional parameter (control) are given. Relation to the classical asymptotical stability is illustrated.
On a Generalized Sturm Theorem
Authors: Portaluri Alessandro
Published: March 2016

Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm type oscillation theorem for indefinite systems with Dirichlet boundary conditions of the form

where pi is a smooth path of matrices on the complex n-dimensional vector space ℂn, p2m is the symmetry represented by the diagonal block matrix diag (In-v, -Iv), and where v is an integer between 0 and n and I is the identity matrix.
Remarks on the 2-Dimensional Lp-Minkowski Problem
Authors: Jiang Mei-Yue
Published: March 2016

Positive periodic solutions of the equation

ẍ + x = g(t)xp-1

are considered with continuous and T-periodic g. Some existence results of solutions are obtained by variational method.
On the Integrability of a Tritrophic Food Chain Model
Authors: Llibre Jaume , Valls Clàudia
Published: March 2016

In this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.
Solutions of the Generalized Rotation-Modified Kadomtsev-Petviashvili Equation
Authors: Chen Jianqing , Liu Yue
Published: March 2016

The rotation-modified Kadomtsev-Petviashvili equation is a modification of the Kadomtsev-Petviashvili (KP) equation widely used to describe the effects of rotation on small-amplitude, long waves propagating in one primary direction. In this paper we investigate conditions for the finite-time blow-up solutions and the uniform bounds of the solution of the generalized rotation-modified Kadomtsev-Petviashvili equation. The conditions are expressed in terms of the energy and the best constant of the anisotropic Sobolev inequality.
On Multiplicity of Positive Solutions for Quasilinear Equation with Co-normal Boundary Condition
Authors: Kaur Bhatia Sumit , Sreenadh K. , Dhanya R.
Published: March 2016

Let Ω ⊂ ℝN, N ≥ 3, be a bounded domain with C2 boundary,

, the critical exponent for the Sobolev imbedding. In this work, we are interested in the following problem:

where λ > 0, 0 ≤ q < p - 1. We show that there exists 0 < Λ < ∞ such that for suitable ranges of p and q, (Pλ) admits at least two solutions in W1,p (Ω) if λ ∈ (0, Λ) and no solution if λ > Λ. The proof of these assertions is done by first finding the local minimum for the variational functional associated to (Pλ) and then applying mountain pass arguments to obtain a saddle point type solution. In the critical case we are considering, there are technical reasons which make the mountain pass argument work for only certain ranges of p and q.
Multiplicity and Existence Results for a Nonlinear Elliptic Equation With Sobolev Exponent
Authors: Bouchech Zakaria , Chtioui Hichem
Published: March 2016

In this paper we consider the following nonlinear elliptic equation with Dirichlet boundary conditions: -Δu = K(x)up, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a smooth domain in ℝn, n ≥ 4 and

is the critical Sobolev exponent. Using dynamical and topological methods involving the study of critical points at infinity we establish, under generic conditions on K, some existence and multiplicity results.
New Results for Finite Morse Index Solutions on ℝN and applications
Authors: Dancer E. N.
Published: March 2016

We prove new results for linearized stable and finite Morse index solutions on ℝN and give applications to half space and bounded domain problems.
Asymptotic Speed of Propagation for Fisher-Type Degenerate Reaction-Diffusion-Convection Equations
Authors: Malaguti Luisa , Ruggerini Stefano
Published: March 2016

The paper deals with the initial value problem for the degenerate reaction-diffusion-convection equation

ut + h(u)ux = (um)xx + f(u), x ∈ ℝ, t > 0,

where h is continuous, m > 1, and f is of Fisher-type. By means of comparison type techniques, we prove that the equilibrium u ≡ 1 is an attractor for all solutions with a continuous, bounded, non-negative initial condition u0(x) = u(x, 0) ≢ 0. When u0 is also compactly supported and satisfies 0 ≤ u0 ≤ 1, the convergence is such that an asymptotic estimate of the interface can be obtained. The employed techniques involve the theory of travelling-wave solutions that we improve in this context. The assumptions on f and h guarantee that the threshold speed wavefront is not stationary and we show that the asymptotic speed of the interface equals this minimal speed.
Backward Blow-up Estimates and Initial Trace for a Parabolic System of Reaction-Diffusion
Authors: Bidaut-Véron Marie-Françoise , García-Huidobro Marta , Yarur Cecilia
Published: March 2016

In this article we study the positive solutions of the parabolic semilinear system of competitive type

in Ω × (0, T), where Ω is a domain of ℝN, and p,q > 0, pq ≠ 1, Despite of the lack of comparison principles, we prove local upper estimates in the superlinear case pq > 1 of the form

u(x, t) ≦ Ct-(p+1)/(pq-1), v(x, t) ≦ Ct-(q+1)/(pq-1)

in ω × (0, T1), for any domain ω ⊂⊂ Ω, T1 ∈ (0, T), and C = C(N, p, q, T1, ω). For p, q > 1, we prove the existence of an initial trace at time 0, which is a Borel measure on Ω. Finally we prove that the punctual singularities at time 0 are removable when p, q ≧ 1 + 2/N.
Microglobal Analysis
Authors: Ehrenpreis Leon
Published: March 2016

We study some Phragmén-Lindelöf type results, which were considered as extensions of maximal modulus theorem. We shall consider them from the viewpoint of Fourier analysis. Our analysis shows that the Phragmén-Lindelöf theorems can be regarded as the convexity of microglobal wave front sets. We prove such theorems for elliptic systems of equations with constant coefficients.
L∞-Bounds for Solutions of Supercritical Elliptic Problems with Finite Morse Index
Authors: Harrabi Abdellaziz , Rebhi Salem
Published: March 2016

We study here finite Morse index solutions of -∆u = f(u) on the entire space or half space and their application to smooth bounded domain problems when the growth of the non-linearity is faster than the usual Sobolev critical exponent.
Remarks on Existence of Large Solutions for p-Laplacian Equations with Strongly Nonlinear Terms Satisfying the Keller-Osserman Condition
Authors: Goncalves J. V. A. , Zhou Jiazheng
Published: March 2016

We deal with existence of large solutions of ∆pu = a(x)f(u)+b(x)g(u) in ℝN. It is shown that if a, b, f, g are non-negative real valued functions with a, b ∈ C(ℝN), f, g ∈ C([0,∞)) and f + g ≥ h where h is a continuous, non-negative, non- decreasing function satisfying the Keller-Osserman condition then the equation above admits a large solution if the equation -∆pv = a(x) + b(x) in ℝN has a positive upper solution decaying to zero at infinity. No monotonicity condition is required from either f or g. Our proof is based on the method of lower and upper-solutions. We extend recent results by A. V. Lair and A. Mohammed.
Periodic Solutions of a Singular Equation With Indefinite Weight
Authors: Bravo José Luis , Torres Pedro J.
Published: March 2016

Motivated by some relevant physical applications, we study the existence and uniqueness of T-periodic solutions for a second order differential equation with a piecewise constant singularity which changes sign. Other questions like the stability and robustness of the periodic solution are considered.
Variational Inequalities with General Multivalued Lower Order Terms Given by Integrals
Authors: Khoi Vy
Published: March 2016

This paper is about the existence and some properties of solutions of variational inequalities associated with the 2nd order inclusion

div[A(x, ∇u)] + L ∈ f (x, u) in Ω,

where the lower order term f (x, u) is a general multivalued function. Both coercive and noncoercive cases are considered. In the noncoercive case, we use a sub-supersolution approach to study the existence, comparison, and other properties of the solution set such as its compactness, directedness, and the existence of extremal solutions.
Multiple Solutions for the p(x)− Laplace Operator with Critical Growth
Authors: Silva Analia
Published: March 2016

The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δp(x)u = |u|q(x)−2u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p∗(x)} ≠ ø, where p∗(x) = Np(x)/(N − p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u|p(x)−2∇u) is the p(x)−laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.
Periodic Solutions of Systems with Singularities of Repulsive Type
Authors: Amster Pablo , Maurette Manuel
Published: March 2016

Motivated by the classical Coulomb central motion model, we study the existence of T-periodic solutions for the nonlinear second order system of singular ordinary differential equations u′′ + g(u) = p(t). Using topological degree methods, we prove that when the nonlinearity g : ℝN\{0} →ℝN is continuous, repulsive at the origin and bounded at infinity, if an appropriate Nirenberg type condition holds then either the problem has a classical solution, or else there exists a family of solutions of perturbed problems that converge uniformly and weakly in H1 to some limit function u. Furthermore, under appropriate conditions we prove that u is a classical solution.
A Note on the Complete Rotational Invariance of Biradial Solutions to Semilinear Elliptic Equations
Authors: Abatangelo L. , Terracini S.
Published: March 2016

We investigate symmetry properties of solutions to equations of the form

-Δu =

+ f(|x|, u)

in ℝN for N ≥ 4, with at most critical nonlinearities. By using geometric arguments, we prove that solutions with low Morse index (namely 0 or 1) and which are biradial (i.e. are invariant under the action of a toric group of rotations), are in fact completely radial. A similar result holds for the semilinear Laplace-Beltrami equations on the sphere. Furthermore, we show that the condition on the Morse index is sharp. Finally we apply the result in order to estimate best constants of Sobolev type inequalities with different symmetry constraints.
Equivalence of Some Multi-Valued Elliptic Variational Inequalities and Variational-Hemivariational Inequalities
Authors: Carl Siegfried
Published: March 2016

First, we prove existence and comparison results for multi-valued elliptic variational inequalities involving Clarke’s generalized gradient of some locally Lipschitz functions as multi-valued term. Only by applying the definition of Clarke’s gradient it is well known that any solution of such a multi-valued elliptic variational inequality is also a solution of a corresponding variational-hemivariational inequality. The reverse is known to be true if the locally Lipschitz functions are regular in the sense of Clarke. Without imposing this kind of regularity the equivalence of the two problems under consideration is not clear at all. The main goal of this paper is to show that the equivalence still holds true without any additional regularity, which will fill a gap in the literature. Existence and comparison results for both multi-valued variational inequalities and variational-hemivariational inequalities are the main tools in the proof of the equivalence of these problems.
Stability and the Growth of the Number of Closed Characteristics on Compact Convex Hypersurfaces
Authors: Liu Hui
Published: March 2016

In this paper, we study relationship between the stability and the growth of the number of closed characteristics on compact convex hypersurfaces in ℝ2n, and also the stability of closed characteristics on compact convex hypersurfaces in ℝ2n under some pinching conditions.
A Variational Approach to a Nonlocal Elliptic Problem with Sign-Changing Nonlinearity
Authors: Corrêa Francisco Julio S.A. , Delgado Manuel , Suárez Antonio
Published: March 2016

In this paper we are concerned with the nonlocal elliptic problem

where Ω ⊂ℝN is a bounded smooth domain, f, g : ℝ →ℝ are given functions and p is a fixed real number. We use variational methods to prove multiplicity results.
On the Existence of Three Nontrivial Solutions for Periodic Problems Driven by the Scalar p-Laplacian
Authors: Papageorgiou Nikolaos S. , Papalini Francesca
Published: March 2016

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential function. First we establish an alternative minimax expression for the first nonzero eigenvalue for the negative periodic scalar p-Laplacian and then using it we prove the existence of three nontrivial solutions, two of which have constant sign. Our approach is variational, based on the nonsmooth critical point theory.
Heteroclinic Solutions to Asymptotically Autonomous Equations via Continuation Methods
Authors: Gavioli Andrea
Published: March 2016

By means of a continuation argument, we prove the existence of at least one increasing heteroclinic solution to a scalar equation of the kind ẍ = a(t)V′(x), where V is a non-negative double well potential, and a(t) is a positive, measurable coefficient, which is definitively monotone with respect to |t|, converges to l as |t| diverges and fulfils one of the two following assumptions: a(t) ≥ l everywhere, or a(t) − l converges to 0, as |t| → +∞, more slowly than a suitable exponential term.
Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms
Authors: Abdellaoui Boumediene , Dall’Aglio Andrea , Peral Ireneo , Léon Sergio Segura de
Published: March 2016

In the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum:

where 1 < p < N, Ω is a bounded open subset of ℝN (N ≥ 2), Δpu = div(|∇u|p−2∇u) is the so called p-Laplacian operator,

sign s ., ϕ(ν0) ∈ L1(Ω), μ is a finite Radon measure and f ∈ L∞(Ω×(0, T)) for every T > 0. Then we apply this existence result to show wild nonuniqueness for a connected nonlinear parabolic problem having a gradient term with natural growth.
Smoothness of Asymptotic Phase Revisited
Authors: Battelli Flaviano , Palmer Kenneth J.
Published: March 2016

It is well-known that solutions on the stable manifold of a hyperbolic periodic solution of an autonomous system of ordinary differential equations have an asymptotic phase which has the same order of smoothness as the vector field. In this paper we show if the system depends on a parameter that, in general, the asymptotic phase loses one order of smoothness in the parameter.
Existence and Uniqueness of Solutions for a Class of p-Laplace Equations on a Ball
Authors: Korman Philip
Published: March 2016

For a class of equations generalizing the model case

Δpu − a(r)up−1 + b(r)uq = 0 in B, u = 0 on∂B,

where B is the unit ball in Rn, n ≥ 1, r = |x|, p, q > 1, and Δp denotes the p-Laplace operator, we give conditions for the existence and uniqueness of positive solution. In case n = 1, we give a more general result.
A Biharmonic Equation in ℜ4 Involving Nonlinearities with Subcritical Exponential Growth
Authors: Sani Federica
Published: March 2016

In this paper we consider a biharmonic equation of the form Δ2u+V(x)u = f (u) in the whole four-dimensional space ℜ4. Assuming that the potential V satisfies some symmetry conditions and is bounded away from zero and that the nonlinearity f is odd and has subcritical exponential growth (in the sense of an Adams’ type inequality), we prove a multiplicity result. More precisely we prove the existence of infinitely many nonradial sign-changing solutions and infinitely many radial solutions in H2(ℜ4). The main difficulty is the lack of compactness due to the unboundedness of the domain ℜ4 and in this respect the symmetries of the problem play an important role.
Potential Estimates for Quasi-Linear Parabolic Equations
Authors: Liskevich Vitali , Skrypnik Igor I. , Sobol Zeev
Published: March 2016

For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wolff potentials.
On the Convergence of Solutions of Globally Modified Navier-Stokes Equations with Delays to Solutions of Navier-Stokes Equations with Delays
Authors: Marín-Rubio Pedro , Real José , Márquez-Durán Antonio M.
Published: March 2016

We prove that under suitable assumptions, from a sequence of solutions of Globally Modified Navier-Stokes equations with delays we can extract a subsequence which converges in an adequate sense to a weak solution of a three-dimensional Navier-Stokes equation with delays. An additional case with a family of different delays involved in the approximating problems is also discussed.
Global Bifurcations of Critical Orbits via Equivariant Conley Index
Authors: Rybicki Sławomir
Published: March 2016

Let V be a finite-dimensional representation of a compact connected Lie group G and let ϕ : V × [λ1, λ2] → ℝ be a family of G-invariant potentials of the class C2 such that ∇vϕ(0, λ) = 0 for every λ ∈ [λ1, λ2], where ∇vϕ is the gradient of ϕ with respect to the first coordinate. Denote by V′i a direct sum of eigenspaces of the isomorphism ∇v
2 ϕ(0, λi) corresponding to positive eigenvalues, i = 1, 2. We have proved that if dimV′1 ≧ dimV′2 and the representation V′1 is not equivalent (as a linear representation of G) to the representation V′2 ⊕ ℝ[2k], k ∈ {0} ∪ ℕ (where ℝ[2k] is a 2k-dimensional trivial representation of G), then there is a global bifurcation of G-orbits of non-zero solutions of problem ∇vϕ(v, λ) = 0 from the interval {0} × [λ1, λ2]. We have proved that a global bifurcation and symmetrybreaking of solutions phenomenon occurs simultaneously for elliptic differential equations considered by Smoller and Wasserman in [25], which improves results of [25].
Blow up Points and the Morse Indices of Solutions to the Liouville Equation in Two-Dimension
Authors: Takahashi Futoshi
Published: March 2016

We consider the Liouville equation

−Δu = λeu in Ω, u =0 on∂Ω,

on a smooth bounded domain Ω in ℝ2, where λ > 0 is a parameter. Let {un} be an m-point blowing up solution sequence of the problem for λ = λn ↓ 0, which satisfies

for m ∈ℕ. We prove that the number of blow up points m is less than or equal to the Morse index of un for n sufficiently large.

As a corollary, we show that if a solution un of Morse index one has the property that

, then the number of blow up points of the sequence is exactly one. Note that in the last result, we do not need any geometrical assumption such as the convexity of the domain.
Nonexistence Results of Sign-changing solutions for a Supercritical Problem of the Scalar Curvature Type
Authors: Ould Bouh Kamal
Published: March 2016

This paper is devoted to the study of the nonlinear elliptic problem with supercritical critical exponent (Pε) : −Δu = K|u|4/(n−2)+εu in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 3, K is a C3 positive function and ε is a positive real parameter. We show first that in dimension 3, for ε small, (Pε) has no sign-changing solutions with low energy which blow up at two points. For n ≥ 4, we prove that there are no sign-changing solutions which blow up at two nearby points. We also show that (Pε) has no bubble-tower sign-changing solutions.
Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane
Authors: Fonda Alessandro , Toader Rodica
Published: March 2016

By the use of a generalized version of the Poincaré-Birkhoff fixed point theorem, we prove the existence of at least two periodic solutions for a class of Hamiltonian systems in the plane, having in mind the forced pendulum equation as a particular case. Our approach is closely related to the one used by Franks in [15], but the proof remains at a more elementary level.
Asymptotic Approach to Inverse Bifurcation for Nonlinear Sturm-Liouville Problems
Authors: Shibata Tetsutaro
Published: March 2016

We consider the nonlinear inverse bifurcation problem

−u′′(t) + f (u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0,

where λ > 0 is a positive parameter, and the nonlinear term f (u) is unknown. We show that, if the asymptotic behavior of the Lq-bifurcation curve λ = λq(α) (1 ≤ q < ∞) of the positive solutions is understood well, then we are able to obtain f (u) and to characterize the asymptotic behavior of f(u) as u → ∞.
Dual Spaces of Weighted Multi-Parameter Hardy Spaces Associated with the Zygmund Dilation
Authors: Han Xiaolong , Lu Guozhen , Xiao Yayuan
Published: March 2016

In this paper, we apply the discrete Littlewood-Paley-Stein analysis to prove the duality theorem of weighted multi-parameter Hardy spaces associated with Zygmund dilations, i.e., (HpZ (ω))∗ = CMOZ
p (ω) for 0 < p ≤ 1. Our theorems extend the HZ
p - CMOZ
p duality theorems established in [13] (see also [12]) for non-weighted multi-parameter Hardy spaces associated with the Zygmund dilation.
On Variational Inequalities Driven by Elliptic Operators Not in Divergence Form
Authors: Matzeu Michele , Servadei Raffaella
Published: March 2016

In this paper we study semilinear variational inequalities driven by an elliptic operator not in divergence form modeled by

where Ω is a bounded domain of RN, N ≥ 3, with smooth boundary, A is the elliptic operator, not in divergence form, given by

Here aij, ai , i,j = 1,...,N , and a0 satisfy suitable regularity conditions, while 1 < s < 4/(N − 2) and the obstacle ψ is a function sufficiently smooth. Even if this problem is not variational in nature, we will prove the existence of non-trivial non-negative solutions for it, performing a variational approach combined with a penalization technique. This kind of approach seems to be new for problems of this type. We also prove a C1,α-regularity result for the solutions of our problem.
Solitary Waves and Vortices in Non-Abelian Gauge Theories with Matter
Authors: Benci Vieri , Bonanno Claudio
Published: March 2016

We consider a non-Abelian gauge theory in ℝ4 equipped with the Minkowski metric, which provides a model for the interaction between a bosonic matter field and a gauge field with gauge group S U(2). We prove the existence of solitary waves which are related to those found for the Klein-Gordon-Maxwell equations.