bluuebunny/crossref_metadata_2025_split huggingface dataset:
Existence and Stability of Standing Waves For Schrödinger-Poisson-Slater Equation
Authors: Kikuchi Hiroaki 
Published: March 2016

Abstract
We study the existence and stability of standing wave for the Schrödinger-Poisson-Slater equation in three dimensional space. Let p be the exponent of the nonlinear term. Then we first show that standing wave exists for 1 < p < 5. Next, we show that when 1 < p < 7/3 and p ≠ 2, standing wave is stable for some ω > 0. We also show that when 7/3 < p < 5, standing wave is unstable for some ω > 0. Furthermore, we investigate the case of p = 2. We prove these results by using variational methods.
On Existence of L∞-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term
Authors: Goncalves J.V. , Melo A.L. , Santos C.A. 
Published: March 2016

Abstract
We establish new results concerning existence and the behavior at infinity of solutions for the singular nonlinear elliptic equation −Δu = ρa(x)u−α + λb(x)uγ in ℝN, where a, b are nonnegative Hölder continuous functions with a + b > 0, α,γ > 0 are constants and ρ, γ are positive parameters. We emphasize that powers uγ with γ ≤ 1 were treated earlier by a number of authors. Our results address mainly terms uγ, where γ is any number bigger than one which we name strongly nonlinear. Penalty arguments, variational principles and an approximation procedure will be exploited.
Global Existence for Quadratic Systems of Reaction-Diffusion
Authors: Desvillettes Laurent , Fellner Klemens , Pierre Michel , Vovelle Julien 
Published: March 2016

Abstract
We prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of L log L-entropy type holds. The approach relies on an a priori dimension-independent L2-estimate, valid for a wider class of systems including also some classical Lotka-Volterra systems, and which provides an L1-bound on the nonlinearities, at least for not too degenerate diffusions. In the more degenerate case, some global existence may be stated with the use of a weaker notion of renormalized solution with defect measure, arising in the theory of kinetic equations.
A Multiplicity Result Including Sign-Changing Solutions For a Nonlinear Elliptic Problem in RN
Authors: Hirano Norimichi , Shioji Naoki 
Published: March 2016

Abstract
We show that the problem

has multiple solutions including sign-changing ones, where μ > 0, N ≥ 3, 1 < p < (N + 2)/(N − 2) and Q : ℝN → ℝ is some continuous function. We obtain signchanging solutions which are not only local minimum types in N* but also mountain pass types in N*, where N* = {u = u+ +u− ∈ H1(ℝN) : u+ ≠ 0, u− ≠ 0, ∫ℝN (|∇u±|2 + μ|u±|2) dx = ∫ℝN Q(x)|u±|p+1 dx}.
On a Minimization Problem Involving the Critical Sobolev Exponent
Authors: Prinari Francesca , Visciglia Nicola 
Published: March 2016

Abstract
Following [3] we study the following minimization problem:

in any dimension n ≥ 4 and under suitable assumptions on a(x). Mainly we assume that a(x) belongs to the Lorentz space Ln/2 ,d(Ω) and the set
N ≡ {x ∈ Ω|a(x) < 0}
has positive Lebesgue measure. Notice that this last condition is satisfied when the set N has a nontrivial interior part (in fact this is the typical assumption imposed in the literature on the set N).
Soliton Solutions to a Class of Quasilinear Elliptic Equations on ℝ
Authors: Alves M.J. , Carrião P.C. , Miyagaki O.H. 
Published: March 2016

Abstract
This paper is concerned with the existence of positive solutions for a class of quasilinear elliptic equations on ℝ. The results are proved by combining the concentration-compactness principle due to Lions with a minimization approach.
Multiplicity of Solutions For p-Laplacian Equations Which Need Not be Coercive
Authors: Filippakis Michael E. , Papageorgiou Nikolaos S. 
Published: March 2016

Abstract
In this paper, we consider nonlinear Dirichlet problem driven by the p-Laplacian differential operator. Using variational methods based on the critical point theory and truncation techniques, we prove the existence of at least three nontrivial smooth solutions. The hypotheses on the nonlinearity incorporate in our framework of analysis both coercive and noncoercive problems. For the semilinear problem (p = 2), using Morse theory, we show the existence of four nontrivial smooth solutions.
Positive and Nodal Solutions For a Nonlinear Schrödinger Equation with Indefinite Potential
Authors: Furtado Marcelo F. , Maiay Liliane A. , Medeiros Everaldo S. 
Published: March 2016

Abstract
We deal with the nonlinear Schrödinger equation
-Δu + V(x)u = f(u) in ℝN,
where V is a (possible) sign changing potential satisfying mild assumptions and the nonlinearity f ∈ C1(ℝ, ℝ) is a subcritical and superlinear function. By combining variational techniques and the concentration-compactness principle we obtain a positive ground state solution and also a nodal solution. The proofs rely in localizing the infimum of the associated functional constrained to Nehari type sets.
Asymptotic Behavior of The Unique Solution to a Singular Elliptic Problem With Nonlinear Convection Term And Singular Weight
Authors: Zhang Zhijun 
Published: March 2016

Abstract
By Karamata regular variation theory, we first derived the exact asymptotic behavior of the local solution to the problem -φʹʹ(s) = g(φ(s)), φ(s) > 0, s ∈ (0, a) and φ(0) = 0. Then, by a perturbation method and constructing comparison functions, we derived the exact asymptotic behavior of the unique classical solution near the boundary to a singular Dirichlet problem -Δu = b(x)g(u) + λ|▽u|q, u > 0, x ∈ Ω, u|aΩ = 0, where Ω is a bounded domain with smooth boundary, λ ∈ ℝ, q ∈ [0, 2]; g ∈ C1((0, ∞), (0, ∞)), is decreasing in (0, ∞) with lims→0 + g(s) = +∞; the weight b is positive in Ω and singular on the boundary.
Morse Indices of Closed Geodesics on Katok's 2-Spheres
Authors: Long Yiming , Wang Wei 
Published: March 2016

Abstract
In this paper, we compute precisely Morse indices of iterates of the two closed geodesics on the 2-sphere with Katok’s metric. This information is used to give a direct proof for the Poincaré series of the free loop space on S2.
The Multidimensional Bipolar Quantum Drift-diffusion Model
Authors: Chen Xiuqing , Guo Yingchun 
Published: March 2016

Abstract
We investigate the bipolar quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions. First, we establish the global weak solution with large initial value and periodic boundary conditions. Then we show the semiclassical limit by using new methods based on delicate interpolation estimates and compactness argument. Furthermore, when the doping profile is a constant, we find that the weak solution approaches its mean value exponentially as time increases to infinity.
Vortices with Prescribed L2Norm in the Nonlinear Wave Equation
Authors: Badiale Marino , Rolando Sergio 
Published: March 2016

AbstractWe prove the existence of rotating solitary waves (vortices) with enough largely prescribed L2norm for the nonlinear Klein-Gordon equation with nonnegative potential, which makes the equation suitable for physical models and guarantees the well-posedness of the corresponding Cauchy problem. This is done by finding nonnegative cylindrical solutions to the standing equationwhere x = (y, z) ∈ ℝk× RN–k, N > k ≥ 0 and μ > 0 is the fundamental eigenvalue, namely, the Lagrange multiplier of the minimization problem(with infimum over a suitable subspace of H1(ℝN)).
Existence and Multiplicity of Solutions for Neumann p-Laplacian-Type Equations
Authors: Gasiński Leszek , Papageorgiou Nikolaos S. 
Published: March 2016

Abstract
We consider nonlinear Neumann problems driven by p-Laplacian-type operators which are not homogeneous in general. We prove an existence and a multiplicity result for such problems. In the existence theorem, we assume that the right hand side nonlinearity is p-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. In the multiplicity result, when specialized to the case of the p-Laplacian, we allow strong resonance at infinity and resonance at 0.
The Porous Medium Equation With Blowing Up Boundary Data
Authors: T. Osvaldo Venegas 
Published: March 2016

Abstract
We study the blow-up set of a solution u(x, t) to the porous medium equation, ut = Δ(um), in Ω × (0, T) for two different boundary conditions, u(x, t) = f(x)/(T - t)

or

(x, t) = g(x)/(T - t)

on ӘΩ × (0, T). Here m > 1 and Ω is a bounded smooth domain in ℝN. We establish point-wise and integral conditions on f and g respectively in order to obtain regional or global blow-up.
On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains
Authors: Al Sayed Waad , Véron Laurent 
Published: March 2016

Abstract
We study the existence and uniqueness of the positive solutions of the problem (P): Әtu - Δu + uq = 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L1(Ω), when Ω is a bounded domain in ℝN. We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N - 2) and it is unique if ӘΩ = ӘΩ̅c. If ӘΩ has the local graph property, we prove that there exists at most one solution to problem (P).
Asymptotic Analysis of a Radionuclide Transport Model With Unbounded Viscosity
Authors: Choquet Catherine 
Published: March 2016

Abstract
We consider a model describing compressible nuclear waste disposal contamination in porous media. The transport of brine and radionuclides is described by a nonlinear coupled degenerate parabolic system. The viscosity of the fluid is unbounded and concentrations and temperature dependent. We study the asymptotic behavior of the model for little Peclet numbers.
Periodic Perturbations With Delay of Autonomous Differential Equations on Manifolds
Authors: Furi Massimo , Spadini Marco 
Published: March 2016

Abstract
We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the crucial step, in order to cope with the delay, we define a suitable (infinite dimensional) notion of Poincaré T-translation operator and prove a formula that, in the unperturbed case, allows the computation of its fixed point index.
Periodic and Bloch Solutions to a Magnetic Nonlinear Schrödinger Equation
Authors: Clapp Mónica , Iturriaga Renato , Szulkin Andrzej 
Published: March 2016

Abstract
We study the equation
(℘A) (-i▽ + A)2u + V u = |u|p-2u,
where A ∈C1,α(ℝN,ℝN) and V ∈C0,α(ℝN) are 2π-periodic in each variable, V > 0; and p ∈(2; 2*) with 2* := ∞ if N = 2 and

We address two questions: first, the gauge-dependence problem for 2π-periodic solutions u : ℝN → C and second, the multiplicity of Bloch solutions. Unlike the nonperiodic case where problem (℘A) is basically independent of A (it is gauge invariant), in the periodic case this is far from being true. Under some assumptions on A we show that, if there exists a one-to-one correspondence between the 2π-periodic solutions of (℘A) and those of (℘A + z) preserving their absolute value, then z lies in a subset of measure zero of ℝN. We use this fact to show the existence of an uncountable set of Bloch solutions with real quasimomentum.
Global Continuation for Quasilinear Elliptic Systems on ℝN and the Equations of Elastostatics
Authors: Gebran Hicham G. , Stuart Charles A. 
Published: March 2016

Abstract
We consider quasilinear systems of second order elliptic equations on ℝN. Using a continuation theorem based on the topological degree for C1 - Fredholm maps, we derive global properties of a maximal connected set of solutions which decay exponentially to zero at in¯nity. These results are used to treat a problem concerning the equilibrium of an elastic body occupying the whole space and subjected to a one parameter family of localized external forces.
On Some Quasilinear Critical Problems
Authors: Valeriola Sébastien de , Willem Michel 
Published: March 2016

Abstract
In this paper we prove the almost everywhere convergence of the gradient of Palais-Smale sequences, allowing us to apply the Brezis-Lieb lemma. This leads us to show that infima are attained, and thus to prove the existence of optimal solutions for some critical problems. Our method does not use the concentration- compactness principle.
Ground States and Bound States of a Nonlinear Schrödinger System
Authors: Liu Zhaoli , Wang Zhi-Qiang 
Published: March 2016

Abstract
This paper concerns existence and multiplicity of ground states and bound states of the time-independent Schrödinger system

where n = 2, 3, N ≥ 2, λj > 0 for j = 1, ... , N, βjj > 0 for j = 1, ... , N,
and βij = βji. In the attractive case we give sufficient condition for existence of co-existing ground states with large couplings, and in the repulsive case we prove existence of infinitely many co-existing bound state solutions with arbitrary couplings.
Addendum to the Paper “Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations″, Advanced Nonlinear Studies 6 (2006), 411-436
Authors: Caraballo Tomás , Real José , Kloeden Peter E. 
Published: March 2016

AbstractIn this paper we improve Theorem 7 in [1] which deals with the existence and uniqueness of solutions of the three dimensional globally modified Navier-Stokes equations.
Boundary Behavior of Solutions to Singular Boundary Value Problems for Nonlinear Elliptic Equations
Authors: Zhang Zhijun , Li Xiaohong , Zhao Yuanzhang 
Published: March 2016

Abstract
Let Ω be a bounded domain with smooth boundary in ℝN and h ∈ C((0,∞), (0,∞)) with lims→0+ h(s) = Υ ∈ (0,∞). By the perturbation method, which is due to García Melián, and nonlinear transformations and comparison principles, we derive the exact boundary behavior of solutions to a singular Dirichlet problem

. Then, applying the result, combining two kinds of nonlinear transformations, we derive the exact boundary behavior of solutions to a boundary blow-up elliptic problem and a singular Dirichlet problem, where the weight b is positive in Ω and may be (rapidly) vanishing or blow up on the boundary.
Existence and Concentration of Bound States for a p-Laplacian Equation in ℝN
Authors: Gloss Elisandra 
Published: March 2016

Abstract
We study existence and asymptotic behavior of positive solutions for quasilinear elliptic equations of the form -εpΔpv + V(x)|v|p-2v = f(v) in ℝN, 1 < p < N, as ε → 0. The potential V : ℝN → ℝ has a positive infimum, inf∂ΩV > infΩ V for some bounded domain Ω in ℝN and f is a subcritical nonlinearity without some growth conditions such as Ambrosetti-Rabinowitz.
Global Existence and Blowup for the Cubic Nonlinear Klein-Gordon Equations in Three Space Dimensions
Authors: Zhang Jian , Gan Zaihui , Guo Boling 
Published: March 2016

Abstract
In this paper, we apply a cross-constrained variational method to study the classic nonlinear Klein-Gordon equation with cubic nonlinearity in three space dimensions. By constructing a type of cross-constrained variational problem and establishing the so-called cross invariant manifolds, we obtain a sharp threshold for blowup and global existence of the solution to the equation under study which is different from that in [10] . On the other hand, we give an answer to the question that how small the initial data have to be for the global solutions to exist.
Solitons for the Nonlinear Klein-Gordon Equation
Authors: Bellazzini J. , Benci V. , Bonanno C. , Micheletti A.M. 
Published: March 2016

AbstractIn this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.
Bifurcation of Limit Cycles from a Polynomial Degenerate Center
Authors: Buică Adriana , Giné Jaume , Llibre Jaume 
Published: March 2016

Abstract
Using Melnikov functions at any order, we provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of the degenerate center ẋ = −y((x2 + y2)/2)m and ẏ = x((x2 + y2)/2)m with m ≥ 1, when we perturb it inside the whole class of polynomial vector fields of degree n. The positive integers m and n are arbitrary. As far as we know there is only one paper that provide a similar result working with Melnikov functions at any order and perturbing the linear center ẋ = −y, ẏ = x.
Symmetry Results for Nonvariational Quasi-Linear Elliptic Systems
Authors: Montoro Luigi , Sciunzi Berardino , Squassina Marco 
Published: March 2016

Abstract
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in non-variational form. Moreover, in the two dimensional case, we study the system when set in a half-space.
A Minimum Problem with Free Boundary for the p(x)−Laplace Operator
Authors: Lyaghfouri A. 
Published: March 2016

Abstract
In this paper we consider the problem of minimizing the functional

We prove Lipschitz continuity for each minimizer u and establish the nondegeneracy at the free boundary (∂[u > 0]) ∩ Ω and the locally uniform positive density of the sets [u > 0] and [u = 0]. In particular we obtain that the Lebesgue measure of the free boundary is zero.
Subharmonic Solutions of Planar Hamiltonian Systems: a Rotation Number Approach
Authors: Boscaggin Alberto 
Published: March 2016

Abstract
We prove the existence of infinitely many subharmonic solutions, with prescribed nodal properties, for a planar Hamiltonian system Jz′ = ΔzH(t, z), with H periodic in the first variable. The goal is achieved by performing estimates of the rotation numbers with respect to deformed polar coordinates and applying Ding’s version of the Poincaré-Birkhoff fixed point theorem.
A Legendre Transform on an Exotic S3
Authors: Martino Vittorio 
Published: March 2016

Abstract
We consider an exotic contact form α on S3 and we establish explicitly the existence of a non singular vector field v in ker(α) such that the non-singular one-differential form β(・) := dα(v, ・) is a contact form on S3 with the same orientation as α. In particular this means that a Legendre transform can be completed.
Regularizing Effect of a Gradient Term in a Problem Involving the p-Laplacian Operator
Authors: Perrotta Adamaria , Primo Ana 
Published: March 2016

Abstract
In this article we consider the following problem

with max{p − 1, 1} ≤ q ≤ p < N, Ω a bounded domain and f, g positive measurable functions in Ω. We give assumptions on g with respect to q and p for which for all λ > 0 and all f ∈ L1(Ω), f ≥ 0, problem (P) has a positive solution. In particular, we focus our attention on the case when 0 ∈ Ω and

to prove that the assumptions on g are optimal. Furthermore, regularity results are given.
Multiplicity and Concentration of Positive Solutions for a Class of Quasilinear Problems
Authors: Alves Claudianor O. , Figueiredo Giovany M. 
Published: March 2016

Abstract
In this work we study multiplicity and concentration of nontrivial solutions for the following class of quasilinear problems:
-div(a(|▽u|p)|▽u|p-2▽u) + V(εx)b(|u|p)|u|p-2u=f(u),
where ε is a positive parameter, a, b, f : ℝ → ℝ are C1 functions and V : ℝN →ℝ is a continuous function.
Homogenization of Maximal Monotone Vector Fields via Selfdual Variational Calculus
Authors: Ghoussoub Nassif , Moameni Abbas , Sáiz Ramón Zárate 
Published: March 2016

Abstract
We use the theory of selfdual Lagrangians to give a variational approach to the homogenization of equations in divergence form, that are driven by a periodic family of maximal monotone vector fields. The approach has the advantage of using Γ-convergence methods for corresponding functionals just as in the classical case of convex potentials, as opposed to the graph convergence methods used in the absence of potentials. A new variational formulation for the homogenized equation is also given.
Nonlinear Resonance: a Comparison Between Landesman-Lazer and Ahmad-Lazer-Paul Conditions
Authors: Fonda Alessandro , Garrione Maurizio 
Published: March 2016

Abstract
We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.
A Uniqueness Result for Δu - λu + V(⃒x⃒)uP = 0 on ℝ2
Authors: Genoud François 
Published: March 2016

Abstract
Uniqueness of positive radial solutions decaying at infinity is proved for a class of semilinear elliptic equations on ℝ2. Complementary results for the same kind of equations were obtained in the early 90’s, on ℝN with N ≥ 3, and in finite balls of ℝN with N ≥ 2. The new result presented here plays a crucial role in the global bifurcation problem, previously studied by the author.
Quasilinear Elliptic Problems with General Growth and Nonlinear Term Having Singular Behavior
Authors: El-Hadi Miri Sofiane 
Published: March 2016

AbstractIn this paper we deal with the following quasilinear elliptic problemswhere Ω ⊂ ℝNis a bounded regular domain, d(x) = dist(x, ∂Ω), p > 1, λ > 0 and 0 < ν ≤ p. Moreover, g, q and f are nonnegative functions verifying suitable hypotheses. The main goal of this work is to analyze the interaction between the functions d, g and the gradient term to get existence and nonexistence results. The singular behavior of g near 0 will provide a new phenomenon that does not appear in the case where the absorption term g(u) q(d(x)) is dropped or substituted by a regular one.
Radial Solutions of a Supercritical Elliptic Equation with Hardy Potential
Authors: Guo Zuji , Liu Zhaoli 
Published: March 2016

Abstract
Various properties of radial solutions of the supercritical elliptic equation with Hardy Potential

are studied, where Ω = int{x ∈ ℝN | α ≤ |x| < b}, which is a ball if 0 = α < b < +∞, an annulus if 0 < α < b < +∞, an exterior domain if 0 < α < b = +∞, and the whole space ℝN if α = 0, b = +∞. We assume p is supercritical, that is, p > 2∗ with 2∗ =

being the critical Sobolev exponent, and N ≥ 3.
Count and Symmetry of Global and Local Minimizers of the Cahn-Hilliard Energy Over Cylindrical Domains
Authors: Nascimento Arnaldo Simal do , Biesdorf João , Crema Janete 
Published: March 2016

Abstract
We address the problem of minimization of the Cahn-Hilliard energy functional under a mass constraint over two and three-dimensional cylindrical domains. Although existence is presented for a general case the focus is mainly on rectangles, parallelepipeds and circular cylinders. According to the symmetry of the domain the exact numbers of global and local minimizers are given as well as their geometric profile and interface locations; all are onedimensional increasing/decreasing and odd functions for domains with lateral symmetry in all axes and also for circular cylinders. The selection of global minimizers by the energy functional is made via the smallest interface area criterion.
The approach utilizes Γ−convergence techniques to prove existence of an one-parameter family of local minimizers of the energy functional for any cylindrical domain. The exact numbers of global and local minimizers as well as their geometric profiles are accomplished via suitable applications of the unique continuation principle while exploring the domain geometry in each case and also the preservation of global minimizers through the process of Γ−convergence.