bluuebunny/crossref_metadata_2025_split huggingface dataset:
Semilinear Elliptic Systems With Exponential Nonlinearities in Two Dimensions
Authors: Figueiredo Djairo G. de , Ó João Marcos do , Ruf Bernhard 
Published: March 2016

Abstract
We establish a priori bounds for positive solutions of semilinear elliptic systems of the form

where Ω is a bounded and smooth domain in ℝ2. We obtain results concerning such bounds when f and g depend exponentially with respect to u and v.
Multiple Solutions of Some Nonlinear Variational Problems
Authors: Candela A.M. , Palmieri G. 
Published: March 2016

Abstract
The aim of this paper is to prove some existence and multiplicity results for functionals of type J(u) = ∫Ω­ A(x, u)|▽u|2dx - ∫Ω­ G(x, u)dx, u 2 D ∊ H0
1 (Ω), with bounded domain Ω in ℝN. Since, in general, J is not Gâteaux differentiable in D, we study its restriction on the Banach space X = H0
1 (Ω) ∩ L∞(Ω) and apply some abstract existence and multiplicity theorems involving a variant of condition (C) below.
Normalized Solutions to Strongly Indefinite Semilinear Equations
Authors: Buffoni Boris , Esteban Maria J. , Séré Eric 
Published: March 2016

Abstract
In this paper we discuss the existence of normalized solutions of nonlinear elliptic PDEs in gaps of the essential spectrum of the corresponding differential operator. This issue can he of interest, for instance, in nonlinear optics or in crystalline models with impurities.
Some Notes on Function Spaces and Dirichlet Forms on Self-Similar Sets
Authors: Liu Yuan , Wen Zhi-Ying 
Published: March 2016

Abstract
Grigor’yan, Hu and Lau [10] introduced sub-Gaussian heat kernels on general metric measure spaces and defined a family of function spaces to characterize the domain of associated Dirichlet forms. In this paper, we will improve their results about norm equivalence. As an application, we construct self-similar Dirichlet forms on a class of self-similar sets containing the Sierpiński gaskets and carpets. Then we prove the Poincaré inequality and give effective resistance estimates by the self-similarity. Consequently, we have a new equivalent characterization of heat kernel estimates through function spaces with strong recurrent condition.
Homoclinic Orbits For First Order Hamiltonian Systems With Convex Potentials
Authors: Xu Xiangjin 
Published: March 2016

Abstract
In this paper new estimates on the C0-norm of homoclinic orbit are shown for first order convex Hamiltonian systems possessing super-quadratic potentials. Applying these estimates, some new results on the existence of infinitely many geometrically distinct homoclinic orbits are proved, which generalize the main results in [2] and [10].
Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations
Authors: Caraballo Tomás , Real José , Kloeden Peter E. 
Published: March 2016

Abstract
We prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.
Study of the Singular Yamabe Problem in Some Bounded Domain of ℝn
Authors: Rébaï Yomna 
Published: March 2016

Abstract
In this paper, we extend the result of R. Mazzeo and F. Pacard in the following direction: Given Ω any bounded open regular subset of ℝn, n ≥ 3 and given x1, x2 ∈ Ω, we give a sufficient condition on x1, x2, for the problem

to have a positive weak solution in Ω with 0 boundary data, which is singular at each xi.
On Stable and Meta-stable Solutions of the Shadow System For the Geirer-Meinhardt Equation
Authors: Dancer E.N. 
Published: March 2016

AbstractWe show how the theory of finite Morse index solutions for small diffusion problems can be adapted to the shadow system for the Geirer-Meinhardt equation. In particular, we prove that the only possible stable solution of this shadow system is the one peak solution discussed by Wei and Ni, Takagi and Yanagida.
Symmetry Results For Solutions of a Semilinear Nonhomogeneous Problem
Authors: Mataloni Silvia 
Published: March 2016

Abstract
In this paper we show the axial symmetry of a particular type of solutions of the following semilinear nonhomogeneous problem

where B is the unit ball of ℝN, N ≥ 3,

u+ = 0 if u < 0 and φ1(x) > 0 is the eigenfunction of -Δ corresponding to the first eigenvalue λ1, with Dirichlet boundary conditions. The solutions considered exhibit one or two peaks and concentrate, as the parameter s goes to +∞.
Perturbation of Symmetry and Multiplicity of Solutions For Strongly Indefinite Elliptic Systems
Authors: Tarsi Cristina 
Published: March 2016

Abstract
We consider the following elliptic system:

where Ω ⊂ ℝN, N ≥ 3 is a smooth bounded domain. If h(x) ≡ k(x) ≡ 0, the system presents a natural ℤ2 symmetry, which guarantees the existence of infinitely many solutions. In this paper we show that the multiplicity structure can be maintained if (p,q) lies below a suitable curve in ℝ2.
Maslov-Type Index Theory For Symplectic Paths With Lagrangian Boundary Conditions
Authors: Liu Chun-gen 
Published: March 2016

Abstract
In this paper, we establish an index theory for symplectic paths starting from the identity with a Lagrangian boundary condition. We show that in some sense the index is the intersection number of a Lagrangian path generated by the symplectic path and a constant Lagrangian path. The various properties of this index theory are developed.
Existence of Infinitely Many Solutions For a Class of Semilinear Subelliptic Equations on Rational Carnot Groups
Authors: Loiudice Annunziata 
Published: March 2016

Abstract
We establish the existence of infinitely many solutions for the equation
-ΔGu + u = f(ξ,u), ξ ∈ G
where ΔG is a sublaplacian on a rational Carnot group G. The function f is assumed to be periodic with respect to a discrete co-compact subgroup of G and satisfy subcritical growth conditions.
Asymptotic Behavior of the Steklov Eigenvalues For the p−Laplace Operator
Authors: Pinasco Juan Pablo 
Published: March 2016

Abstract
In this paper we study the asymptotic behavior of the Steklov eigenvalues of the p- Laplacian. We show the existence of lower and upper bounds of a Weyl-type expansion of the function N(λ) which counts the number of eigenvalues less than or equal to λ, and we derive from them asymptotic bounds for the eigenvalues.
Existence and Regularity Results For Some Singular Elliptic Problems
Authors: Leonori Tommaso , Petitta Francesco 
Published: March 2016

Abstract
We are interested in the study of existence, uniqueness and regularity of solutions for nonlinear elliptic problems whose model is the linear boundary value problem

where 0 ∊ Ω. We will prove that such results strongly depend on the size of the lower order term, that is on the constant B.
Computations of Critical Groups and Applications to Nonlinear Differential Equations With Resonance
Authors: Guo Yuxia , Liu Jiaquan 
Published: March 2016

Abstract
In this paper, we develop a method to compute critical groups at degenerate critical points under more general conditions. The abstract results are used to study the existence and multiplicity of nontrivial solutions for nonlinear differential equations with resonance both at infinity and at zero.
On a “Zero Mass” Nonlinear Schrödinger Equation
Authors: Azzollini Antonio , Pomponio Alessio 
Published: March 2016

Abstract
We look for positive solutions to the nonlinear Schrödinger equation
−Ɛ2∆u − V (x)f′(u) = 0
in ℝN, where V is a continuous bounded positive potential and f satisfies particular growth conditions which make our problem fall in the so called “zero mass case”. We prove an existence result for any Ɛ > 0, and a multiplicity result for Ɛ sufficiently small.
The Global Existence and Semiclassical Limit of Weak Solutions to Multidimensional Quantum Drift-diffusion Model
Authors: Chen Xiuqing 
Published: March 2016

Abstract
We establish the global weak solutions to quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions with large initial value and periodic boundary conditions and furthermore obtain the semiclassical limit by entropy estimate and compactness argument.
Dynamics of a Contact Structure Along a Vector Field of its Kernel
Authors: Bahri Abbas , Xu Yongzhong 
Published: March 2016

Abstract
In this paper we prove that in order to define the homology of [3], the hypothesis that there exists a vector field in the kernel of the contact form which defines a dual form with the same orientation is not essential. The technique is quantitative: as we introduce a large amount of rotation near the zeroes of the vector field in the kernel, we track down the modification of the variational problem and provide bounds on a key quantity (denoted by τ).
On the Morse Index of a Functional Arising in Contact Form Geometry
Authors: Bahri Abbas , Xu Yongzhong 
Published: March 2016

Abstract
In this paper we study a functional at infinity associated to a contact form on a three dimensional manifold. The Morse index of this functional at infinity can be decomposed into two parts, one along the characteristic manifold and the other along the normal directions. We prove that we can redistribute the negative directions between the two subspaces through a local deformation of the contact form near a critical point at infinity.
Branching Points For a Class of Variational Equations Involving Potential With Parameter
Authors: Lu Fei 
Published: March 2016

Abstract
In this paper, under the framework of Ambrosetti [1], using mountain-pass theorem and topological degree theory, we extend the result of Ambrosetti [1] (in which H is independent of λ and C1) to the equation
Au + H(λ, u) = λu
with H jointly continuous in (λ, u) and H(λ, ·) of class C0, 1. We give a description of the structure of local bifurcation from isolated eigenvalues of A: the set of bifurcation solutions at each isolated eigenvalue of A contains at least one connected branch. Applications to the existence of branching points to semilinear elliptic partial differential equations are given.
An Elementary Proof of a Characterization of Constant Functions
Authors: De Marco Giuseppe , Mariconda Carlo , Solimini Sergio 
Published: March 2016

Abstract
We give two short and elementary proofs of a characterization of constants function by Brezis. Whereas the original proof involves some refined arguments on Sobolev spaces and BV functions, ours are based either on convolutions or on a sort of nonsmooth Mean Value Theorem which is new to our knowledge.
Weak Solutions of the Problem ∆2u = un/n-4 with Prescribed Singular Sets
Authors: Rébaï Yomna 
Published: March 2016

Abstract
In this paper, we are interested in the following biharmonic equation:

with Navier boundary conditions on ∂Ω; where Ω is an open bounded domain of ℝn, with n ≥ 5, having a smooth boundary, and ∑ ⊂ Ω is either a set of finite number of points of Ω or a smooth closed submanifold of Ω without boundary. We construct positive solutions to this problem which are singular at ∑.
Positive Solutions of a System Arising from Angiogenesis
Authors: Delgado Manuel , Suárez Antonio 
Published: March 2016

Abstract
We study a system of equations arising from angiogenesis which contains a non- regular term that vanishes below a certain threshold. We are forced to modify the usual methods of bifurcation theory because of this loss of regularity. Nevertheless, we obtain results on the existence, uniqueness and permanence of a positive solution for the time-dependent problem; and the existence and uniqueness of a positive solution for the stationary one.
On the Global Analytic Integrability of the Belousov–Zhabotinskii System
Authors: Llibre Jaume , Valls Clàudia 
Published: March 2016

Abstract
The well-known Belousov-Zhabotinskii system can be written as
ẋ = s(x + y - qx2 - xy), ẏ = s-1(-y + fz - xy), ż = w(x - z)
with f, q, s, w ∈ ℝ and s ≠ 0. In this paper we characterize its global analytic first integrals.
Semiclassical Limit For the Nonlinear Klein Gordon Equation in Bounded Domains
Authors: Ghimenti Marco G. , Grisanti Carlo R. 
Published: March 2016

Abstract
We are interested in the existence of standing waves for the nonlinear Klein Gordon equation ε2□ψ + Wʹ(ψ) = 0 in a bounded domain D. A standing wave has the form ψ(t, x) = u(x)e-iwt/ε; for these solutions the Klein Gordon equation becomes

We want to use a Benci-Cerami type argument in order to prove a the existence of several standing waves localized in suitable points of D. The main result of this paper is that, under suitable growth condition on W, for ε suffciently small, we have at least cat(D) stationary solutions of equation (†), where cat(D) is the Ljusternik-Schnirelmann category. The proof is achieved by solving a constrained critical point problem via variational techniques.
Quasilinear Equations With Boundary Blow-up and Exponential Reaction
Authors: García-Melián Jorge 
Published: March 2016

Abstract
We consider the quasilinear elliptic problem Δpu = a(x)eu in a smooth bounded domain Ω of ℝN, with u = +∞ on ӘΩ. Here Δpu = div(|▽u|p-2▽u) is the p-Laplacian operator with p > 1, and a(x) is a continuous positive weight function which can be singular on ӘΩ. Our results include existence, uniqueness and exact boundary behavior of solutions.
On a Fourth Order Elliptic Problem with a Singular Nonlinearity
Authors: Cassani Daniele , Ó João Marcosy do , Ghoussoub Nassif 
Published: March 2016

Abstract
We study the following semilinear biharmonic equation:

, where 0 ≤ f ≤ 1 and BR ⊂ ℝN, N ≥ 1, is the ball centered in the origin of radius R. We prove, under Dirichlet boundary conditions u = Әu/Әƞ = 0 on ӘBR, the existence of λ* = λ*(R, f) > 0 such that for λ ∈ (0, λ*) there exists a minimal (classical) solution u̲λ < which satisfies 0 < u̲λ < 1. In the extremal case λ = λ*, we prove the existence of a weak solution which has finite energy and which is the unique solution even in a very weak sense. For λ > λ* there are no solutions of any kind. Estimates on λ*, stability properties of solutions and nonexistence results in the whole space are also established.
Uniqueness and Characterization of the Maximizers of Integral Functionals With Constraints
Authors: Draghici Cristina , Hajaiej Hichem 
Published: March 2016

AbstractIn this paper we maximize a class of functionals under certain constraints. We find necessary and sufficient conditions for these maximizers to exist and be unique. Moreover, we characterize them and discuss the optimality of our results by constructing counterexamples when one of the hypotheses does not hold.
Positive Solutions for the p-Laplacian and Bounds for its First Eigenvalue
Authors: Bueno H. , Ercole G. , Zumpano A. 
Published: March 2016

Abstract
We prove a result of existence and localization of positive solutions of the Dirich- let problem for -Δpu = w(x)f(u) in a bounded domain Ω, where Δp is the p-Laplacian, w is a weight function and the nonlinearity f(u) satisfies certain local bounds. As in previous results in radially symmetric domains by two of the authors, and in contrast with the hypotheses usually made, no asymptotic behavior is assumed on f. A positive solution is obtained by applying the Schauder Fixed Point Theorem and such approach allows us to construct ordered sub- and super-solutions for the problem, thus producing an iterative method to obtain a positive solution. Our result leads not only to asymptotic conditions on the nonlinearity which provides the existence of a sequence of positive solutions for the problem with arbitrarily large sup norm, but also to an estimate of the first eigenvalue λp(Ω, w) of the p-Laplacian operator with weight w. For w ≡ 1, we compare our lower bound for λp(Ω, 1) with that obtained by means of the Cheeger constant h(Ω). We give a characterization of this constant in terms of the solution of the torsional creep problem -Δpɸp = 1 in Ω with Dirichlet boundary data, which offers a good approximation of the first eigenvalue of the p-Laplacian for p near 1.
Solitary Waves for Quasilinear Schrödinger Equations Arising in Plasma Physics
Authors: Marcos do Ó João , Moameni Abbas 
Published: March 2016

Abstract
We study the quasilinear Schrödinger equation
izt = −∆z +W(x)z − η(|z|2)z − k[∆p(|z|2)]p′(|z|2)z in ℝ2,
where W : ℝ2 →ℝ is a positive potential and the nonlinearity η : ℝ2 × ℝ → ℝ has critical or sub-critical exponential growth. Quasilinear Schrödinger equations of this type have been studied as models of several physical phenomena such as superfluid film equation, in the theory of Heisenberg ferromagnets and magnons, in dissipative quantum mechanics and in condensed matter theory. In a suitable Orlicz space together with Trudinger-Moser inequality we establish an existence of standing wave solutions for this problem. The second order nonlinearity considered in this paper corresponds to the superfluid equation in plasma physics.
Existence of Solution for a Class of Quasilinear Systems
Authors: Alves Claudianor O. , Soares Sérgio H. M. 
Published: March 2016

Abstract
This paper proves the existence of nontrivial solution for a class of quasilinear systems on bounded domains in ℝN, N ≥ 2, whose nonlinearity has a double criticality. The proof is based on a linking theorem without the Palais-Smale condition.
Nodal Solutions for a Singularly Perturbed Nonlinear Elliptic Problem on Riemannian Manifolds
Authors: Micheletti Anna Maria , Pistoia Angela 
Published: March 2016

Abstract
Let (M, g) be a smooth compact Riemannian N−manifold, N ≥ 2. We show that if the scalar curvature of g is not constant, the problem
−ε2∆gu + u = up−1 in M
has a positive solution with two positive peaks ξ1
ε and ξ2
ε, and a sign changing solution with one positive peak η1
ε and one negative peak η2
ε, such that as ε goes to zero Scalg(ξ1
ε), Scalg(η1
ε) →

Scalg(ξ) and Scalg(ξ2
ε), Scalg(η2
ε) →

Scalg(ξ). Here p > 2 if N = 2 and
Radial Solutions for Hamiltonian Elliptic Systems With Weights
Authors: De Nápoli Pablo L. , Drelichman Irene , Durán Ricardo G. 
Published: March 2016

Abstract
We prove the existence of infinitely many radial solutions for elliptic systems in ℝn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent interest.
On the Poincaré-Hopf Theorem for Functionals Defined on Banach Spaces
Authors: Cingolani Silvia , Degiovanni Marco 
Published: March 2016

Abstract
Let X be a reflexive Banach space and f : X → ℝ a Gâteaux differentiable function with f′ demicontinuous and locally of class (S)+. We prove that each isolated critical point of f has critical groups of finite type and that the Poincaré-Hopf formula holds. We also show that quasilinear elliptic equations at critical growth are covered by this result.
On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics
Authors: Giambò Roberto , Giannoni Fabio , Piccione Paolo 
Published: March 2016

Abstract
Let (M, g) be a complete Riemannian manifold, Ω ⊂ M an open subset whose closure is diffeomorphic to an annulus. If ∂Ω is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in Ω̅ = Ω ∪ ∂Ω starting orthogonally to one connected component of ∂Ω and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.
Invariant Manifolds for Random and Stochastic Partial Differential Equations
Authors: Caraballo Tomás , Duany Jinqiao , Lu Kening , Schmalfuβ Björn 
Published: March 2016

Abstract
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic infuences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo- stable and pseudo-unstable manifolds for a class of random partial differential equations and stochastic partial differential equations is shown. Unlike the in- variant manifold theory for stochastic ordinary differential equations, random norms are not used. The result is then applied to a nonlinear stochastic partial differential equation with linear multiplicative noise.
Pseudo Focal Points Along Lorentzian Geodesics and Morse Index
Authors: Javaloyes Miguel Ángel , Masiello Antonio , Piccione Paolo 
Published: March 2016

Abstract
Given a Lorentzian manifold (M, g), a geodesic γ in M and a timelike Jacobi field γ along γ, we introduce a special class of instants along γ that we call γ- pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the γ-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field γ is obtained as the restriction of a globally defined timelike Killing vector field.
Nonuniform Stability of Difference Equations with Infinite Delay
Authors: Barreira Luis , Valls Claudia 
Published: March 2016

Abstract
In this note we consider the notion of nonuniform exponential contraction for delay difference equations with infinite delay (one can argue that the only delay difference equations are those with infinite delay, since otherwise we can always bring them to the standard recurrence form in some higher-dimensional space). We consider the general case of a nonautonomous dynamics. Our main objective is to show that exponential contractions persist under sufficiently small linear and nonlinear perturbations. This includes establishing the continuous dependence with the perturbation of the constants in the notion of contraction. We also characterize the nonuniform exponential contractions in terms of strict Lyapunov sequences, in particular by constructing explicitly a strict Lyapunov sequence for each exponential contraction.
On a Q–Curvature Equation on Complete Riemannian Manifolds
Authors: Maliki Youssef 
Published: March 2016

Abstract
We proceed by variational method to prove the existence of solution of a fourth order partial differential equation on complete non compact manifolds. Sufficient conditions, including the geometry of the manifold, are given to make a minimizing sequence converge to a non trivial solution belonging to Cloc
4,α (M) for some α ∈ (0, 1).
On Ground State Solutions to Mixed Type Singular Semi-Linear Elliptic Equations
Authors: Mohammed Ahmed 
Published: March 2016

Abstract
The purpose of the paper is to establish the existence of ground state solutions to -Δu = ηa(x)f(u)+γb(x)g(u), where the locally Hölder continuous non-negative functions a and b and the non-linearities f and g satisfy some general conditions.
Stability of Closed Characteristics on Compact Hypersurfaces in R2n Under a Pinching Condition
Authors: Wang Wei 
Published: March 2016

Abstract
In this article, let ∑ ⊂R2n be a compact convex hypersurface which is (r,R)-pinched with

. Then ∑ carries at least two strictly elliptic closed characteristics; moreover, ∑ carries at least

non-hyperbolic closed characteristics.