bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Symmetry of Extremals for the Caffarelli-Kohn-Nirenberg Inequalities
Authors: Dolbeaulty Jean , Estebany Maria J. , Lossz Michael , Tarantello Gabriella 
Published: March 2016

Abstract
In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal to 2.
Generic Properties of Singularly Perturbed Nonlinear Elliptic Problems on Riemannian Manifold
Authors: Micheletti Anna Maria , Pistoia Angela 
Published: March 2016

Abstract
Given (M, g) the set {(ε, h) ∈ (0, 1) × Sk : any solution u ∈ A of -ε2 Δg+h u+u = (u+)p-1 on M is non degenerate} is an open dense subset of (0, 1) × Bρ where Bρ is a suitable ball centered at 0 with radius ρ in the Banach space Sk. Here Sk is the space of all Ck symmetric covariant 2-tensors on M and A is a bounded subset of Hg
1 (M) which does not contain the constant function 1.
Existence of Solutions to Quasilinear Elliptic Equations With Singular Weights
Authors: Iturriaga Leonelo , Lorca Sebastian , Montenegro Marcelo 
Published: March 2016

Abstract
In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations with singular weights when the continuous nonlinearity satisfies a superlinear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities.
Coexistence States for Cyclic 3-Dimensional Systems
Authors: Ruiz-Herrera Alfonso 
Published: March 2016

Abstract
We find coexistence states for systems in three dimensions with cyclic dynamic in the boundary of ℝ+
3. This problem had been already studied for competitive systems. In this paper we consider any interaction. This extension seems to be meaningful since the cyclic dynamic on the boundary can appear in natural way in many interactions.
On Best Constants for Limiting Embeddings of Fractional Sobolev Spaces
Authors: Costa David G. , Figueiredo Djairo G. de , Yang Jianfu 
Published: March 2016

Abstract
We consider embeddings of a class of fractional Sobolev spaces Es(Ω) (s ≥ 0) into their limiting Lp(Ω) spaces, for a bounded smooth domain Ω ⊂ ℝN, and study the relationship between the best constants for these embeddings and other best constants corresponding to the case Ω = ℝN.
Forced Duffing Equation With a Resonance Condition
Authors: Tomiczek Petr 
Published: March 2016

Abstract
This article is devoted to the study of the existence of a solution to the periodic nonlinear second order ordinary differential equation with damping
uʺ (x) + cuʹ (x) + g(x,u(x)) = f(x), x ∈ [0, T], u(0) = u(T), uʹ(0) = uʹ(T),
where c ∈ ℝ, g is a Caratheodory function, f ∈ L1([0, T), a quotient

lies between 0 and

and a nonlinearity g satisfies Landesman Lazer type condition near the zero. The techniques we use are a variational method and a critical point theorem.
Asymptotic Symmetry for a Class of Quasi-Linear Parabolic Problems
Authors: Montoro Luigi , Sciunzi Berardino , Squassina Marco 
Published: March 2016

Abstract
We study the symmetry properties of the weak positive solutions to a class of quasi-linear elliptic problems having a variational structure. On this basis, the asymptotic behaviour of global solutions of the corresponding parabolic equations is also investigated. In particular, if the domain is a ball, the elements of the ω limit set are nonnegative radially symmetric solutions of the stationary problem.
A Multiplicity Theorem for Double Resonant Periodic Problems
Authors: Gasiński Leszek , Papageorgiou Nikolaos S. 
Published: March 2016

Abstract
We consider semilinear periodic ordinary differential equations with the nonlinearity exhibiting double resonance at infinity in the spectral interval [λk, λk+1], k ≥ 1. Using minimax methods based on the critical point theory together with Morse theory, we show that the problem has at least four nontrivial solutions.
Normal Geodesics Connecting two Non-necessarily Spacelike Submanifolds in a Stationary Spacetime
Authors: Bartolo R. , Candela A.M. , Caponio E. 
Published: March 2016

Abstract
In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime ℳ. The proof is based on both variational and geometric arguments involving the causal structure of ℳ, the completeness of suitable Finsler metrics associated to it and some basic properties of a submersion. By this interaction, unlike previous results on the topic, also non-spacelike submanifolds can be handled.
Uniformly Elliptic Liouville Type Equations Part II: Pointwise Estimates and Location of Blow up Points
Authors: Bartolucci Daniele , Orsina Luigi 
Published: March 2016

Abstract
We refine the analysis, initiated in [3], [4] of the blow up phenomenon for the following two dimensional uniformly elliptic Liouville type problem in divergence form:

We provide a partial generalization of a result of Y.Y. Li [18] to the case A ≠ I. To this end, in the same spirit of [2], we obtain a sharp pointwise estimate for simple blow up sequences. Moreover, we prove that if {p1, ...,pN} is the blow up set corresponding to a given simple blow up sequence, then,
(∆detA)(pj) = 0, ∀ j = 1, ...,N.
This characterization of the blow up set yields an improvement of the a priori estimates already established in [3].
Bounding Surfaces and Second Order Quasilinear Equations with Compatible Nonlinear Functional Boundary Conditions
Authors: Mawhin Jean , Thompson Bevan 
Published: March 2016

Abstract
We establish existence results for solutions to functional boundary value problems for φ- Laplacian ordinary differential equations assuming there are lower and upper solutions and Lipschitz bounding surfaces for the derivative which we adapt to our problem. Our results apply to some problems which do not satisfy Nagumo growth bounds. Moreover they contain as special cases many results for the p- and ɸ-Laplacians as well as many results where the boundary conditions depend on n-points or even functionals. Our boundary conditions generalize those of Fabry and Habets, Cabada and Pouso, Cabada, O’Regan and Pouso, and many others.
Applications of Sub-Supersolution Theorems to Singular Nonlinear Elliptic Problems
Authors: Loc Nguyen Hoang , Schmitt Klaus 
Published: March 2016

Abstract
The results presented here were motivated by several recent papers on singular boundary value problems for semilinear elliptic equations with convection terms. We present extensions which cover singular nonlinear equations (mainly equations involving the p−Laplacian) containing convection terms. The results obtained are proved using sub- and supersolution theorems (motivated by the results in [18, 19, 20, 23]) and the construction of a well-ordered pair of such using a principal eigenfunction of the p−Laplacian.
On the Well-Posedness of a Class of Vector Schrödinger Equations
Authors: Barile Sara , Squassina Marco 
Published: March 2016

Abstract
We investigate the local and global well-posedness for a class of nonlinear Schrödinger systems with an external time independent electromagnetic field and nonlocal nonlinearities. New conditions related to the growth of the nonlocal term are detected which allow the solvability of the problem.
Estimates of the Green’s Function and its Regular Part on Heisenberg Group Domains
Authors: Gamara Najoua , Guemri Habiba 
Published: March 2016

Abstract
This paper is a preliminary work on Heisenberg group domains, devoted to the study of the Green’s function for the Kohn Laplacian on domains far away from the set of characteristic points. We give some estimates of the Green’s function, its regular part and their derivatives analogous to those proved by A. Bahri, Y.Y. Li, O. Rey in [1], and O. Rey in [16] for Euclidean domains. While the study of such functions on the set of characteristic points of the given domain will be discussed in a forthcoming paper.
On the Persistence of Decay Properties for the b−Family of Equations
Authors: Cai Ying , Gao Hongjun 
Published: March 2016

Abstract
The b−family of equations governs evolution of shallow water waves with the horizontal velocities in different depths related to the parameter b. Using the method of characteristics, we obtain the results of the exponential decay properties of the strong solutions for the b−family of equations. In particular, we show that a non-trivial strong solution with compact initial value can not be compactly supported at any later time.
Regularity of the Extremal Solutions in a Gelfand System Problem
Authors: Cowan Craig 
Published: March 2016

Abstract
We examine the elliptic system given by

where λ, γ are positive parameters and where Ω is a smooth bounded domain in ℝN. Let U denote the parameter region (λ, γ) of strictly positive parameters where (P)λ,γ has a smooth solution and let Υ denote the boundary of U. We show that the extremal solution (u∗, v∗) associated with (λ∗, γ∗) ∈ Υ is smooth provided that 3 ≤ N ≤ 9 and
Location of Bifurcation Points for a Reaction-Diffusion System with Neumann-Signorini Conditions
Authors: Eisner Jan , Väth Martin 
Published: March 2016

Abstract
We consider a reaction-diffusion system of activator-inhibitor or substrate-depletion type in one space dimension which is subject to diffusion-driven instability. We determine the change of bifurcation when a pure Neumann condition is supplemented with a Signorini condition. We show that this change differs essentially from the known case when also Dirichlet conditions are assumed.
Periodic Orbits of Radially Symmetric Systems with a Singularity: the Repulsive Case
Authors: Fonda Alessandro , Toader Rodica 
Published: March 2016

Abstract
We study radially symmetric systems with a singularity of repulsive type. In the presence of a radially symmetric periodic forcing, we show the existence of three distinct families of subharmonic solutions: One oscillates radially, one rotates around the origin with small angular momentum, and the third one with both large angular momentum and large amplitude. The proofs are carried out by the use of topological degree theory.
Liouville Type Theorems for Stable Solutions of Certain Elliptic Systems
Authors: Fazly Mostafa 
Published: March 2016

Abstract
We establish Liouville type theorems for elliptic systems with various classes of nonlinearities on ℝN. We show, among other things, that a system has no semi-stable solution in any dimension, whenever the infimum of the derivatives of the corresponding non-linearities is positive. We give some immediate applications to various standard systems, such as the Gelfand, and certain Hamiltonian systems. The case where the infimum is zero is more interesting and quite challenging. We show that any C2(ℝN) positive entire semi-stable solution of the following Lane-Emden system,

is necessarily constant, whenever the dimension N < 8 + 3α +

, provided p = 1, q ≥ 2 and f (x) = (1 + |x|2)

. The same also holds for p = q ≥ 2 provided

We also consider the case of bounded domains Ω ⊂ ℝN, where we extend results of Brown et al. [1] and Tertikas [18] about stable solutions of equations to systems. At the end, we prove a Pohozaev type theorem for certain weighted elliptic systems.
On the Diffeomorphisms Between Banach and Hilbert Spaces
Authors: Idczak Dariusz , Skowron Andrzej , Walczak Stanislaw 
Published: March 2016

Abstract
In this paper, we give some sufficient conditions for f : X → H to be a diffeomorphism, where X is a Banach space and H is a Hilbert space. The proof of the result is based on the mountain pass theorem. Using this result, in the final part of the paper, we prove an existence theorem for some class of integro-differential equations.
Multiple Non Semi-Trivial Solutions for Elliptic Systems
Authors: Chang Kung-Ching , Wang Zhi-Qiang 
Published: March 2016

Abstract
This is a continuation of our previous paper Chang, Wang, Zhang [6]. We investigate the multiple non semi-trivial solutions for nonlinear elliptic systems by two kinds of index theory. In particular the pseudo index theory for the Z2 × Z2 index theory is developed
The Brezis–Nirenberg Problem for the Hénon Equation: Ground State Solutions
Authors: Secchi Simone 
Published: March 2016

Abstract
This work is devoted to the Dirichlet problem for the equation −Δu = λu + |x|α|u|2*−2u in the unit ball of ℝN. We assume that λ is bigger than the first eigenvalues of the laplacian, and we prove that there exists a solution provided α is small enough. This solution has a variational characterization as a ground state.
The Sturm-Liouville Hierarchy of Evolution Equations II
Authors: Johnson Russell , Zampogni Luca 
Published: March 2016

AbstractIn a previous paper [15] we introduced the Sturm-Liouville (SL) hierarchy of evolution equations. This hierarchy includes the Korteveg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchies. We also defined and discussed in detail the algebro-geometric solutions of the SL-hierarchy. In this paper, we broaden the class of algebro-geometric solutions in a substantial way. Namely, we define and discuss solutions of the SL-hierarchy lying in an isospectral class of the Sturm-Liouville problem −(pφ′)′ + qφ = λyφ, which is determined by data related to a Riemann surface of “infinite genus”.
Global Sign-changing Solutions of a Higher Order Semilinear Heat Equation in the Subcritical Fujita Range
Authors: Galaktionov Victor A. , Mitidieri Enzo , Pohozaev Stanislav I. 
Published: March 2016

Abstract
A detailed study of two classes of oscillatory global (and blow-up) solutions was began in [20] for the semilinear heat equation in the subcritical Fujita range

with bounded integrable initial data u(x, 0) = u0(x). This study is continued and extended here for the 2mth-order heat equation, for m ≥ 2, with non-monotone nonlinearity

with the same initial data u0. The fourth order biharmonic case m = 2 is studied in greater detail. The blow-up Fujita-type result for (0.2) now reads as follows: blow-up occurs for any initial data u0 with positive first Fourier coefficient:
∫ u0(x) dx > 0,
i.e., as for (0.1), any such arbitrarily small initial function u0(x) leads to blow-up. The construction of two countable families of global sign changing solutions is performed on the basis of bifurcation/branching analysis and a further analytic-numerical study. In particular, a countable sequence of bifurcation points of similarity solutions is obtained:
On Nonuniformly Subelliptic Equations of Q−sub-Laplacian Type with Critical Growth in the Heisenberg Group
Authors: Lam Nguyen , Lu Guozhen , Tang Hanli 
Published: March 2016

Abstract
Let ℍn = ℝ2n × ℝ be the n−dimensional Heisenberg group,

be its subelliptic gradient operator, and ρ (ξ) = ( |z|4 + t2 )1/4 for ξ = (z, t) ∈ ℍn be the distance function in ℍn. Denote ℍ = ℍn, Q = 2n + 2 and Q′ = Q/(Q − 1). Let Ω be a bounded domain with smooth boundary in ℍ. Motivated by the Moser-Trudinger inequalities on the Heisenberg group, we study the existence of solution to a nonuniformly subelliptic equation of the form

where f : Ω × ℝ → ℝ behaves like exp ( α |u|Q′ ) when |u| → ∞. In the case of Q−sub- Laplacian

we will apply minimax methods to obtain multiplicity of weak solutions.
Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry
Authors: Bates Peter , Fuscoy Giorgio , Smyrnelis Panayotis 
Published: March 2016

Abstract
We prove the existence of solutions to three-fold symmetric elliptic systems in ℝ2 which have six-fold symmetry, asymptotically approaching each of three minima of the potential as |x| → ∞ in two antipodal sectors of angle π/3.
A Resonant-Superlinear Elliptic Problem Revisited
Authors: Cuesta Mabel , De Coster Colette 
Published: March 2016

Abstract
We consider the resonant-superlinear elliptic problem -Δu = λ1u + (u+)q + f (x), with Dirichlet boundary conditions on a bounded regular domain of ℝN. We assume that

with s > N satisfies ∫Ωfφ1 < 0 and (λ1, φ1) is the first eigenpair of −Δ on H1
0(Ω). We apply a non-well ordered lower and upper solution result on a family of modified problems and obtain a sequence of localized solutions of these modified problems. Thanks to this localization and a precise bootstrap argument we are abble to prove that for large modification, these solutions are, in fact, solutions of our initial problem. The problem was already considered in [2] by a totally different approach.
Qualitative Properties and Existence of Sign Changing Solutions with Compact Support for an Equation with a p-Laplace Operator
Authors: Dolbeault Jean , García-Huidobro Marta , Manasevich Raul 
Published: March 2016

Abstract
We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of variables in the phase plane corresponding to an asymptotic Hamiltonian system and provides qualitative properties of the solutions.
Prevalence of Non-degenerate Periodic Solutions in the Forced Pendulum Equation
Authors: Ortega Rafael 
Published: March 2016

Abstract
Many known properties of the forced pendulum equation are generic. This means that they hold on a residual set of forcings. The classical duality category/measure inspires the main question in the paper: are these properties also valid for a prevalent set of forcings? This is the case for a key property: the non-degeneracy of periodic solutions. The main tool in the proof is a prevalent version of the parametric transversality theorem.
A Continuation Result for Forced Oscillations of Constrained Motion Problems with Infinite Delay
Authors: Benevieri Pierluigi , Furi Massimo , Pera Maria Patrizia , Calamai Alessandro 
Published: March 2016

Abstract
We prove a global continuation result for T-periodic solutions of a T-periodic parametrized second order retarded functional differential equation on a boundaryless compact manifold with nonzero Euler-Poincaré characteristic. The approach is based on the fixed point index theory for locally compact maps on ANRs. As an application, we prove the existence of forced oscillations of retarded functional motion equations defined on topologically nontrivial compact constraints. This existence result is obtained under the assumption that the frictional coefficient is nonzero, and we conjecture that it is still true in the frictionless case.
Pullback Attractors for 2D Navier-Stokes Equations with Delays and Their Regularity
Authors: García-Luengo Julia , Marín-Rubio Pedro , Real José 
Published: March 2016

Abstract
In this paper we obtain some results on the existence of solution, and of pullback attractors, for a 2D Navier-Stokes model with finite delay studied in [4] and [6]. Actually, we prove a result of existence and uniqueness of solution under less restrictive assumptions than in [4]. More precisely, we remove a condition on square integrable control of the memory terms, which allows us to consider a bigger class of delay terms (for instance, just under a measurability condition on the delay function leading the delayed time). After that, we deal with dynamical systems in suitable phase spaces within two metrics, the L2 norm and the H1 norm. Moreover, we prove that under these assumptions, pullback attractors not only of fixed bounded sets but also of a set of tempered universes do exist. Finally, from comparison results of attractors we establish relations among them, and under suitable additional assumptions we conclude that these families of attractors are in fact the same object.
Critical Hyperbolas and Multiple Symmetric Solutions to Some Strongly Coupled Elliptic Systems
Authors: Guedes de Figueiredo Djairo , Moreira dos Santos Ederson , Miyagaki Olímpio Hiroshi 
Published: March 2016

Abstract
We are interested in the existence of multiple symmetric solutions to the Lane-Emden system with Hénon type weights

Here B stands for the open unit ball in ℝN centered at zero, N ≥ 3, α, β ≥ 0, p, q > 0. In this paper we present a complete picture of the quantitative study of solutions to the system above.
Existence and Concentration of Positive Ground State Solutions for Schrödinger-Poisson Systems
Authors: Wang Jun , Tian Lixin , Xu Junxiang , Zhang Fubao 
Published: March 2016

Abstract
In this paper, we study the existence and concentration of positive ground state solutions for the semilinear Schrödinger-Poisson system

where ε > 0 is a small parameter and λ ≠ 0 is a real parameter, f is a continuous superlinear and subcritical nonlinearity. Suppose that b(x) has a maximum. We prove that the system has a positive ground state solution

for all λ ≠ 0 and sufficiently small ε > 0. Moreover, for each λ ≠ 0 we show that uε converges to the positive ground state solution of the associated limit problem and concentrates to a maximum point of b(x) in certain sense as ε → 0. Furthermore, we obtain some sufficient conditions for the nonexistence of positive ground state solutions.
Existence Results for the Prescribed Webster Scalar Curvature on Higher Dimensional CR Manifolds
Authors: Yacoub Ridha 
Published: March 2016

Abstract
This paper is about prescribing the Webster scalar curvature on a compact CR manifold of dimension 2n+1 ≥ 5, which is locally CR equivalent to the standard CR unit sphere S2n+1. The associated variational problem being noncompact we approach this issue with techniques from the critical points at infinity theory, combined with topological tools. Our existence results are based on a generalized Bahri-Coron type criteria. We also give an upper bound on the Morse index of the obtained solutions.
Infinitely Many Solutions for Quasilinear Elliptic Problems with Broken Symmetry
Authors: Bartolo Rossella 
Published: March 2016

Abstract
The aim of this paper is investigating the existence of solutions of the quasilinear elliptic Problem

where Ω is an open bounded domain of RN with C2 boundary ∂Ω, Δpu = div(|∇u|p−2∇u), 1 < p < q < p∗, f ∈ C(Ω̅) and ϕ ∈ C2(Ω̅). By means of the so-called Bolle’s method in [3, 4], we extend a result in [10] where the authors consider Ω =]0, 1[N and u = 0 on ∂Ω.
Liouville-type Theorems for Fully Nonlinear Elliptic Equations and Systems in Half Spaces
Authors: Lu Guozhen , Zhu Jiuyi 
Published: March 2016

Abstract
The main purpose of this paper is to establish Liouville-type theorems and decay estimates for viscosity solutions to a class of fully nonlinear elliptic equations or systems in half spaces without the boundedness assumptions on the solutions. Using the blow-up method and doubling lemma of [18], we remove the boundedness assumption on solutions which was often required in the proof of Liouville-type theorems in the literature. We also prove the Liouville-type theorems for supersolutions of a system of fully nonlinear equations with Pucci extremal operators in half spaces. Liouville theorems and decay estimates for high order elliptic equations and systems have also been established by the authors in an earlier work [15] when no boundedness assumption was given on the solutions.