bluuebunny/crossref_metadata_2025_split huggingface dataset:
Existence of Nonnegative Solutions For a Class of p-Laplacian Equations in IRN
Authors: Dai Shuang , Yang Jianfu 
Published: March 2016

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Topological Remarks–Critical Points at Infinity and String Theory
Authors: Bahri Abbas 
Published: March 2016

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
An Asymptotical Stability in Variational Sense for Second Order Systems
Authors: Idczak Dariusz , Walczak Stanisław 
Published: March 2016

Abstract
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

Abstract
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.
On the Integrability of a Tritrophic Food Chain Model
Authors: Llibre Jaume , Valls Clàudia 
Published: March 2016

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Asymptotic Speed of Propagation for Fisher-Type Degenerate Reaction-Diffusion-Convection Equations
Authors: Malaguti Luisa , Ruggerini Stefano 
Published: March 2016

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Variational Inequalities with General Multivalued Lower Order Terms Given by Integrals
Authors: Khoi Vy 
Published: March 2016

Abstract
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.