bluuebunny/crossref_metadata_2025_split huggingface dataset:
Symmetry of C1 Solutions of p-Laplace Equations in ℝN
Authors: Damascelli Lucio , Rarnaswarny Mythily 
Published: March 2016

Abstract
In this paper we consider positive C1 solutions of the equation - div(|Du|p-2Du)= f(u) in ℝN, vanishing at infinity, in the case 1 < p ≤ 2, f locally Lipschitz continuous in (0, ∞). We prove that the solutions are radially symmetric under two different sets of assumptions on the behaviour of f near zero. In the first case we assume that f is nonincreasing in (0, s0), s0 > 0, and improve a previous result of the authors and Pacella [7] where the symmetry was proved under the hypothesis u ∈ C1(ℝN) ⋂ W1,p(ℝN). In the second case, previously studied when p = 2, we assume that f(u) = O(uα+1) (u → O), and prove the radial symmetry of the solution u, provided

at infinity with m(α+2-p) > p. These results extend to pLaplace equations, 1 < p < 2, analogous symmetry results previously known in the case of strictly elliptic equations. The proofs exploit some Poincaré and Hardy-Sobolev type inequalities
Regularity of Interfaces for an Inhomogeneous Filtration Equation
Authors: Guedda M. , Hilhorst D. , Shmarev S.I. 
Published: March 2016

Abstract
We study the regularity of the interfaces for solutions of the degenerate parabolic equation p(x)ut =(um)xx, m > 1. AS opposed to the classical Porous Medium Equation, the interfaces in this equation may propagate with infinite speed and disappear within a finite time. We establish conditions on the initial function u(x, 0) and the function p(x) sufficient to provide the local C1-regularity of the interfaces until the moment of their disappearance. The interface equation (Darcy's law) is derived.
On a semilinear Robin problem involving critical Sobolev exponent
Authors: Cao Daomin , Noussair Ezzat S. , Yan Shusen 
Published: March 2016

Abstract
We establish the existence of solutions of the problem

under various assumptions on the level sets of Q(x), where Ω is a smooth bounded domain in ℝN, N ≥ 3, Q(x) 0, and a(x) are smooth functions. We also show that if a(x) ≥ a0 > 0 and a0 is suiliciently large, our solutions are not ground states.
On the Principal Eigenvalue of Disconjugate BVPs with L1-Coefficients
Authors: Degla Guy 
Published: March 2016

Abstract
Establishing some general results on the principal eigenvalues for a class of multipoint boundary value problems, we prove existence and uniqueness theorems for positive solutions of nonlinear multipoint boundary value problems. Our argument is based mainly on the maximum principle [4] (highlighting new ordered Banach spaces of continuous functions) and on the continuity of the spectral radius mapping for compact linear operators.
Fujita’s Exponent for a Semilinear Wave Equation with Linear Damping
Authors: Kirane Mokhtar , Qafsaoui Mahmoud 
Published: March 2016

Abstract
We discuss the critical exponent problem for the semilinear wave equation with linear damping
utt +(-1)m|x|αΔmu + ut = f(t,x)|u|p + w(t,x), t > 0, x ∈ℝn,and show that it coincides with the Fujita exponent for the heat equation with the same nonlinearity.
Existence and Multiplicity of Positive Solutions for a Dirichlet Boundary Value Problem in ℝ2
Authors: Barutello V. , Capietto A. , Habets P. 
Published: March 2016

Abstract
We deal with the Dirichlet boundary value problem associated to a parameter-dependent second order vector differential equation. Using the method of lower and upper solutions together with degree theory, we provide existence and multiplicity of positive solutions.
Stability of travelling waves for degenerate reaction-diffusion equations of KPP-type
Authors: Biró Zsolt 
Published: March 2016

Abstract
The aim of this paper is to investigate the asymptotic behaviour as t → ∞ of the solutions to the Cauchy problem for the nonlinear degenerate KPP-type diffusion-reaction equation ut = (um)xx + up - uq, where m,p and q are positive parameters. Our result is similar to the corresponding one of Kolmogorov, Petrowsky and Piscunov; namely, we prove that for a wide class of initial functions, the solution approaches V(x - c*t) as t → ∞ uniformly in x, where V is a travelling-wave solution with a minimal speed c*.
Initial trace of positive solutions to semilinear parabolic inequalities
Authors: Marcus Moshe , Vgron Laurent 
Published: March 2016

Abstract
We study the existence and properties of the initial trace, at t = 0, of positive solutions of ut - ∆u + g(x, t, u) ≥ 0 in Ω × (0, T), where g(x, t, u) > 0 for (x, t ) ∈ Ω × (0, T) and u > 0. We prove that, under some general conditions on g , this initial trace is a Borel measure (which may blow up on compact sets). In addition we derive pointwise estimates for the blow up of solutions at initial singular points. Finally these results are applied to the cases g(., t, r) = tα|r|q-1r (α > 0 ) , and g(., t, r ) = e-1/t|r|q-1r. In this last case we exhibit a new type of full initial blow-up.
Multiple Solutions for Perturbed Elliptic Equations in Unbounded Domains
Authors: Salvatore A. 
Published: March 2016

Abstract
We look for solutions of a nonlinear perturbed Schrödinger equation with nonhomogeneous Dirichlet boundary conditions. By using a perturbation method introduced by Bolle, we prove the existence of multiple solutions in spite of the lack of the symmetry of the problem.
Solitary Waves with Non-Vanishing Angular Momentum
Authors: Benci Vieri , Visciglia Nicola 
Published: March 2016

Abstract
In this paper we prove the existence of infinitely many solitary waves with non vanishing angular momentum for Nonlinear Schrödinger Equation:

where ψ, : ℝ3 × ℝ → ℂ and 2 < p < 6.
On Existence and Concentration of Solutions for a Class of Hamiltonian Systems in ℝN
Authors: Alves C.O. , Soares S.H.M. , Yangt Jianfu 
Published: March 2016

Abstract
In this paper we are concerned with the existence of solutions for the Hamiltonian system

where N ≥ 3, Q, K : ℝN → ℝ are bounded positive continuous functions and the numbers p, q > 1 satisfy

Using dual variational methods we show that under certain conditions on Q and K the system (S∊) has a positive solution which concentrates as ∊ → 0 in a point xo ∈ ℝN where related functionals realize its minimum energy.
Asymptotic Estimates of the First Eigenvalue of the p-Laplacian
Authors: Colbois Bruno , Matei Ana-Maria 
Published: March 2016

Abstract
We consider a 1-parameter family of hyperbolic surfaces M(t) of genus ν which degenerate as t → 0 and we obtain a precise estimate of λ1,p(t), the first eigenvalue of the p-Laplacian (p > 1) on M(t). In some cases we also give a precise estimate of the first eigenfunctions.
As a direct application, we obtain that the quotient

(which is invariant under scaling of the metric) is unbounded even on the set of Riemannian manifolds with constant sectional curvature. This is to our knowledge, the first example of a family of manifolds with this property.
To prove our results we use in an essential way the geometry of hyperbolic surfaces which is very well known. We show that an eigenfunction for λ1,p(t) of Lp norm one is almost constant in the Lp sense (as t → 0) on the parts of M(t) with large injectivity radius, and we estimate precisely its p-energy on the parts with small injectivity radius.
Existence and Nonexistence of Positive Solutions of Indefinite Elliptic Problems in ℝN
Authors: Schneider Matthias 
Published: March 2016

Abstract
Our purpose is to find positive solutions u ∈ D1,2 (ℝN) of the semilinear elliptic problem -Δu - λV(x)u = h(x)up-1 for 2 < p. The functions V and h may have an indefinite sign and the linearized operator need not have a fist (principal) eigenvalue, e.g. we allow V ≡ 1. We give precise existence and nonexistence criteria, which depend on λ and on the growth of h- and h+/V+. Existence theorems are obtained by constrained minimization. The mountain pass theorem leads to a second solution.
Varying Stoichiometric Exponents I: Classical Steady-States and Metasolutions
Authors: López-Gómez Julián 
Published: March 2016

Abstract
This paper characterizes the existence of classical solutions for a class of semilinear elliptic boundary value problems of logistic type whose stoichiometric coefficient is allowed to vary within the region where the reaction takes place. Most of the effort will be focused on the problem of the existence of metasolutions; large solutions extended by infinity that are the main candidates for describing the dynamics of the model in the absence of classical steady-states.
Geodesics in Static Lorentzian Manifolds with Critical Quadratic Behavior
Authors: Bartolo R. , Candela A.M. , Flores J.L. , Sánchez M. 
Published: March 2016

Abstract
The aim of this paper is t o study the geodesic connectedness of a complete static Lorentzian manifold (M.〈·, ·〉L) such that. if K is its irrotational timelike Killing vector field, the growth of β = -〈K, K〉L is (at most) quadratic. This is shown to be equivalent to a critical variational problem on a Riemannian manifold, where some geometrical interpretations yield the optimal results. Multiplicity of connecting geodesics is studied, especially in the timelike case, where the restrictions for the number of causal connecting geodesics are stressed. Extensions to the non-complete case, including discussions on pseudoconvexity, are also given.
On the Quadratic Endomorphisms of the Plane
Authors: Bofill F. , Garrido J.L. , Vilamajó F. , Romero N. , Rovella A. 
Published: March 2016

Abstract
In this article we establish the following result: if a nondegenerate quadratic endomorphism of the plane has no fixed points, then every point has empty omega-limit set and alpha-limit set. It is also shown that there exists a six parameter family open and dense in the space of all quadratic mappings of the plane (even those having fixed points). The degenerate case (when the quadratic forms of both components are linearly dependent), for which the theorem fails, is considered in the last section.
A Seven-Positive-Solutions Theorem for a Superlinear Problem
Authors: Gaudenzi Marcellino , Habets Patrick , Zanolin Fabio 
Published: March 2016

Abstract
We consider the superlinear boundary value problem
uʺ + aμ(t)uγ+1 = 0, u(0) = 0, u(1) = 0,
where γ > 0 and aμ(t) is a sign indefinite weight of the form a+(t)−μa−(t). We prove, for μ positive and large, the existence of 2k − 1 positive solutions where k is the number of positive humps of aμ(t) which are separated by k − 1 negative humps. For sake of simplicity, the proof is carried on for the case k = 3 yielding to 7 positive solutions. Our main argument combines a modified shooting method in the phase plane with some properties of the blow up solutions in the intervals where the weight function is negative.
Combining Linear and Nonlinear Diffusion
Authors: Delgado M. , López-Gómez J. , Suárez A. 
Published: March 2016

Abstract
In this paper we study a generalized porous medium equation where the diffusion rate, say m(x) -spatially heterogeneous- is assumed to be linear, m = 1, on a piece of the support domain, Ω1 and slow nonlinear, m(x) > 1, in its complement, Ωm := Ω \ Ω̄1. More precisely, we characterize the existence of positive solutions and construct the corresponding global bifurcation diagram as one of the parameters of the model changes, showing that a continuous transition occurs between the diagrams of the completely linear case (Ω = Ω1) and of the completely nonlinear case (­Ωm = Ω­). As a result, the effect of a localized slow diffusion rate with varying support is completely characterized. Our analysis is imperative in order to design porous media multi-components systems with changing diffusion rates.
Non-Existence Results for the Coupled Klein-Gordon-Maxwell Equations
Authors: D’Aprile Teresa , Mugnai Dimitri 
Published: March 2016

Abstract
In this paper we obtain some non-existence results for the Klein-Gordon equation coupled with the electrostatic field. The method relies on the deduction of some suitable Pohožaev identity which provides necessary conditions to get existence of nontrivial solutions. The case of Maxwell-Schrödinger type coupled equations is also considered.
On the Ambrosetti-Rabinowitz Superlinear Condition
Authors: Liu Zhaoli , Wang Zhi-Qiang 
Published: March 2016

Abstract
We present various results on multiple solutions for superlinear elliptic equations in a bounded domain or in the whole space. With a Nehari type condition assumed, we show that the standard Ambrosetti-Rabinowitz superlinear condition can be replaced by a more natural super-quadratic condition.
Existence of Multiple Positive Solutions for N-Laplacian in a Bounded Domain in ℝN
Authors: Prashanth S. , Sreenadh K. 
Published: March 2016

Abstract
Let Ω be a bounded domain in ℝN, N ≥ 2, λ > 0, q∊(0, N −1) and

In this article we show the existence of at least two positive solutions for the following quasilinear elliptic problem with an exponential type nonlinearity:

We use Monotonicity and Variational methods to obtain this multiplicity result.
Symmetrization and Mass Comparison for Degenerate Nonlinear Parabolic and Related Elliptic Equations
Authors: Vázquez Juan Luis 
Published: March 2016

Abstract
We consider the solutions to various nonlinear parabolic equations and their elliptic counterparts and prove comparison results based on two main tools, symmetrization and mass concentration comparison. The work focuses on equations like the porous medium equation, the filtration equation and the p-Laplacian equation. The results will be used in a companion work in combination with a detailed knowledge of special solutions to obtain sharp a priori bounds and decay estimates for wide classes of solutions of those equations.
Some Existence Results on Nontrivial Solutions of the Prescribed Mean Curvature Equation
Authors: Le Vy Khoi 
Published: March 2016

Abstract
The paper is concerned with an eigenvalue problem for the prescribed mean curvature equation. We formulate the problem as a variational inequality and show that under some growth conditions on the lower order term, the relaxed problem has at least two nontrivial solutions in a space of functions of bounded variation when the parameter is small.
Existence of Solutions for Some Classes of Singular Hamiltonian Systems
Authors: Alves Claudianor O. , Corrêa Francisco J. S. A. , Gonçalves Jose V. A. 
Published: March 2016

Abstract
This paper deals with existence of positive solution for the following singular Hamiltonian system

where Ω ⊂ ℝN , N ≥ 2, is a smooth bounded domain and H, T, S, K are continuous functions. A key role is played by the Galerkin method.
Rotation Numbers and Global Bifurcation in Systems of Ordinary Differential Equations
Authors: Ward James R. 
Published: March 2016

Abstract
Global bifurcation in boundary value problems for systems of ordinary differential equations is studied. Rotation numbers are associated with solutions and are shown to be invariant along bifurcating continua. This invariance is then used to analyze the global structure of the bifurcating continua, and to demonstrate the existence of infinitely many solutions to some boundary value problems.
Fixed Points for Dissipative-Repulsive Systems and Topological Dynamics of Mappings Defined on N-dimensional Cells
Authors: Pireddu Marina , Zanolin Fabio 
Published: March 2016

Abstract
We prove a fixed point theorem for continuous mappings which satisfy a compression-expansion condition on the boundary of a N-dimensional cell of ℝN. Our work is motivated by a previous theorem of Andres, Gaudenzi and Zanolin (1990) dealing with the existence of periodic solutions for dissipative-repulsive systems and is also related to some recent results by Zgliczyński and Gidea (2004) concerning covering relations for Markov partitions. Applications are given to the study of the iterates of a continuous map of ℝN. In this case we obtain some theorems on the existence of periodic points and chaotic-like dynamics.
Multiplicity of Entire Solutions For a Class of Almost Periodic Allen-Cahn Type Equations
Authors: Alessio Francesca , Montecchiari Piero 
Published: March 2016

Abstract
We consider a class of semilinear elliptic equations of the form
−Δu(x,y) + a(εx)Wʹ(u(x,y)) = 0, (x,y) ∊ ℝ2 (0.1)
where ε > 0, a : ℝ → ℝ is an almost periodic, positive function and W : ℝ → ℝ is modeled on the classical two well Ginzburg-Landau potential W(s) = (s2 - 1)2. We show via variational methods that if ε is sufficiently small and a is not constant then (0.1) admits infinitely many two dimensional entire solutions verifying the asymptotic conditions u(x, y) → ±1 as x → ±∞ uniformly with respect to y ∊ ℝ.
Bifurcation and Concentration of Radial Solutions of a Nonlinear Degenerate Elliptic Eigenvalue Problem
Authors: Evéquoz G. , Stuart C.A. 
Published: March 2016

Abstract
We consider the nonlinear boundary-value problem in ℝN (N ≥ 3),

where C ∊ C1 ([0, 1]) with C(r) > 0 for all r ∊ [0, 1]; C(0) = 0 and

and, for some T > 0; f ∊ C1([-T, T]) is an odd function that is strictly concave on [0, T] with f(0) = f(T) = 0 and f′(0) = 1. We prove that there is vertical bifurcation of radial solutions at every

in the sense that there exists a sequence {(λ, wn)} of solutions such that

These solutions concentrate at 0 in the sense that wn(0) = T for all n but wn converges uniformly to zero on all compact subsets that do not contain zero.
Asymptotic Behaviour of the Gradient of Large Solutions to Some Nonlinear Elliptic Equations
Authors: Alessio Porretta , Laurent Véron 
Published: March 2016

Abstract
If h is a nondecreasing real valued function and 0 ≤ q ≤ 2, we analyse the boundary behaviour of the gradient of any solution u of −Δu + h(u) + |∇u|q = f in a smooth N-dimensional domain Ω with the condition that u tends to infinity when x tends to ∂Ω. We give precise expressions of the blow-up which, in particular, point out the fact that the phenomenon occurs essentially in the normal direction to ∂Ω. Motivated by the blow-up argument in our proof, we also give a symmetry result for some related problems in the half space.
Regularity of Entropy Solutions of Quasilinear Elliptic Problems Related to Hardy-Sobolev Inequalities
Authors: Abdellaoui Boumediene , Colorado Eduardo , Sanchón Manel 
Published: March 2016

Abstract
This article is concerned with the regularity of the entropy solution of

where Ω is a smooth bounded domain Ω of ℝN such that 0 ∈ Ω, 1 < p < N. and γ < (N-p)/p. Assuming f ∈ Lq(Ω, |x|α(q-1)dx) for some q ≥ 1 and Nγp/(N-p) ≤ α ≤ (γ+1)p, we obtain estimates for the entropy solution u and its weak gradient in Lebesgue spaces with weights. Moreover, we introduce some explicit examples showing the optimality of our results and a relation between our problem and a Hardy-Sobolev type inequality.
Non-Degeneracy and Periodic Solutions of Semilinear Differential Equations with Deviation
Authors: Meng Gang , Yan Ping , Lin Xiaoyan , Zhang Meirong 
Published: March 2016

Abstract
In this paper, we will use some Sobolev constants to construct certain classes of nondegenerate potentials for linear differential equations with deviation. As an application of these potentials, we will give some existence results of periodic solutions of semilinear equations with deviation.
Isolated Singularities of Solutions of Quasilinear Anisotropic Elliptic Equations
Authors: Namlyeyeva Yuliya V. , Shishkov Andrey E. , Skrypnik Igor I. 
Published: March 2016

Abstract
We consider a wide class of degenerate quasilinear second order elliptic equations with model representative

, whose solutions have singularity at a point. There are established sharp point-wise conditions for removable isolated singularity of solutions of such equations. For solutions with non-removable point singularity (source type or fundamental solution), precise upper and lower estimates near the singularity point are obtained.
Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient
Authors: Ferone Vincenzo , Messano Basilio 
Published: March 2016

Abstract
In this paper we study the Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = H(x, u, Du), where the principal term is a Leray-Lions operator defined on W0
1,p (Ω), and H(x, u, Du) grows with respect to Du at most like |Du|q, p-1 ≤ q ≤ p. Comparison results are obtained between the rearrangement of a solution u of Dirichlet problem quoted above and the rearrangement of the solution of a problem whose data are radially symmetric.
Topological Translations and Nonlinear Resonance
Authors: Dambrosio Walter , Ortega Rafael 
Published: March 2016

Abstract
In this paper we study resonance for nonlinear oscillators from a topological point of view. The Poincaré map associated to a linear second order equation at resonance is a translation of the plane. Our aim is to prove that in the case of nonlinear equations the Poincaré map is topologically conjugate to a translation. The proof is based on a characterization of translations in terms of Lyapunov functions.
Existence and Multiplicity of Positive Solutions For a Class of Elliptic Boundary Value Problems in the Half-Space
Authors: Hsu Tsing-San 
Published: March 2016

Abstract
In this paper, we prove that if b(x) satisfies some suitable conditions, then -Δu + u = b(x)up in ℝN
+ with the boundary condition u(xʹ, 0) = λg(xʹ) has at least two positive solutions if 0 < λ < λ*, a minimal positive solution if λ = λ* and no positive solution if λ > λ*.
Back to the Keller-Osserman Condition for Boundary Blow-up Solutions
Authors: Dumont Serge , Dupaigne Louis , Goubet Olivier , Rădulescu Vicentiu 
Published: March 2016

Abstract
This article is concerned with the existence, uniqueness and numerical approximation of boundary blow up solutions for elliptic PDE’s Δu = f(u), where f satisfies the so-called Keller-Osserman condition. We characterize existence of such solutions for non-monotone f. As an example, we construct an infinite family of boundary blow up solutions for the equation Δu = u2(1 + cos u) on a ball. We prove uniqueness (on balls) when f is increasing and convex in a neighborhood of infinity and we discuss and perform some numerical computations to approximate such boundary blow-up solutions.
On Algebro-Geometric Solutions of the Camassa-Holm Hierarchy
Authors: Zampogni Luca 
Published: March 2016

Abstract
We find global solutions of algebro geometric type for all the equations of a new commuting hierarchy containing the Camassa-Holm equation. This hierarchy is built in analogy to the classical K-dV and AKNS hierarchies. We use a zero curvature method to give recursion formulas. The time evolution of the solutions is completely determined, and the motion on a nonlinear subvariety Υ of a generalized Jacobian variety is obtained by solving an inverse problem for the Sturm-Liouville equation L(φ) = −φ″ + φ = λyφ. This is the natural setting for the expression of the solutions which depend linearly with respect to t and x, with coordinates on a curvilinear parallelogram contained in such a subvariety φ. φ is obtained as the restriction of the generalized Abel map I0 to the space Symmg(R) of unordered g-tuples of points on R, and the nonlinear parallelogram is the image through the restricted generalized Abel map of the moving poles Pi(x, t) (i = 1, . . . , g) of the Weyl m-functions m±(x, t, λ) of the dynamical Sturm-Liouville family of equations Lx(φ) = −φ″ + φ = λτx(y)φ, where τ is the translation flow. It turns out that the choice of a particular stationary initial condition ug(x, t0) completely determines the solution u(x, t) of all the equations in the hierarchy, as functions of the poles Pi(x, t) of the Weyl m-functions corresponding to the family Lx of Sturm-Liouville operators, with density function y(x, t) = uxx(x, t)/2 − 2u(x, t). For every t∊ℝ, the maps x ↦ y(x, t) lie in an isospectral class of the associated family of Sturm-Liouville equations Lx(φ), and are completely determined by assigning spectral parameters and initial conditions for the poles Pi(x, t).