bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Prescribed Scalar Curvature on a 3 - Dimensional CR Manifold
Authors: Gamara Najoua 
Published: March 2016

Abstract
We extend to the CR framework an equivalent problem to the well known Kazdan- Warner problem on Riemannian manifolds. Let (M, θ) be a three-dimensional pseudo Hermitian CR compact manifold, locally conformally CR equivalent to the sphere S3 of C4. We give suitable conditions on a C3 positive function K, defined on M, to be the Webster scalar curvature for a contact form on M conformal to θ.
Necessary and Sufficient Conditions for the Oscillation of Planar like-Lienard Systems
Authors: Granados Bertha , Tineo Antonio 
Published: March 2016

Abstract
In this paper we consider the planar system x' = f (x, y), y' = -g(x, y), where f-1(0) is the graph of a function F and g(x, y)x > 0 for x ≠ 0, and we study the intersection of the trajectories of the system with the curves y = F(x) and x = 0. We improve some results in the line of [I], [4] and [3].
Multiplicity results for systems of asymptotically linear second order equations
Authors: Capietto Anna , Dalbono Francesca 
Published: March 2016

Abstract
We prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.
Removable Singularities and Existence for a Quasilinear Equation with Absorption or Source Term and Measure Data
Authors: Bidaut-Véron Marie Françoise 
Published: March 2016

Abstract
We study the properties of the following equations with absorption or source term
-Δpu = ± |u|q-1 u + μ,
in a domain Ω of ℝN, where 1 < p < N, q > p-1, and μ is a Radon measure on Ω. We introduce a notion of local entropy solution, and give necessary conditions on μ for the existence of solutions, in terms of capacity. The question of removability of sets is also considered, as well as some stability results. Finally we give existence results in ℝN for the case of absorption.
Absence of Solutions for Some Elliptic Equations and Systems in Half-Space with Nonlinear Neumann Boundary Conditions
Authors: Eric Nabana 
Published: March 2016

Abstract
This work deals with the nonexistence of solutions of the semilinear elliptic equation -Δu = a(x)|u|p in ℝN
+ = { x = ( x1 , . . . , xN) ∈ ℝN : xN > 0 ) , with the boundary condition

on ∂ℝN
+ = {(xʹ, 0) : xʹ ∈ ℝN-1}, where a(x) ≥ 0, b(xʹ) ≥ 0, p > 1 and q > 1. We are also concerned with a nonexistence result for the system -Δui = ai(x)|ui+1|pi, x ∈ ℝN
+ , 1 ≤ i ≤ m, um+1 = u1 with

on ∂ℝN
+ , where ai(x) ≥ 0 and pi > 1.
Perturbation of Global Solution Curves for Semilinear Problems
Authors: Korman Philip , Li Yi , Ouyang Tiancheng 
Published: March 2016

Abstract
We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in [6]. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.
On the Existence of Positive Solutions of Slightly Supercritical Elliptic Equations
Authors: Molle Riccardo , Passaseo Donato 
Published: March 2016

Abstract
In this paper we deal with existence and multiplicity of solutions for problem P(ε, Ω) below, in bounded domains Ω which do not satisfy some symmetry prop erties that play an important role in the proof of previous results on this subject. For ε > 0 small and k large enough, we construct solutions blowing up, as ε → 0, at exactly k points which approach the boundary of Ω as k tends to infinity.
We also present some examples showing that solutions of this type also exist in some contractible domains which may be even very close to starshaped domains.
A Priori Estimates for Solutions of "Sub-critical" Equations on CR Sphere
Authors: Prajapat J. , Ramaswamy Mythily 
Published: March 2016

Abstract
Here we study the precise blow-up behaviour and obtain a priori estimates for the finite energy C2-solutions of the equation

on the odd dimensional spheres S2n+1 with standard CR structure, as the exponent

for p ∈

, Q = 2n + 2 is the homogeneous dimension.
Non-simultaneous Blow-up in a Nonlinear Parabolic System
Authors: Quirós Fernando , Rossi Julio D. 
Published: March 2016

Abstract
We prove the existence of a nontrivially coupled parabolic system such that one of its components becomes unbounded at a finite time while the other remains bounded, a situation that we denote as non-simultaneous blow-up. Our system consists of two porous medium equations with coupled nonlinear flux boundary conditions. As a preliminary step, we will obtain a necessary and sufficient condition for blow-up. Next we characterize completely, in the case of increasing in time solutions, the set of parameters appearing in the system for which nonsimultaneous blow-up indeed occurs. In the course of our proofs we will obtain a necessary and sufficient condition for the blow-up of solutions to general porous medium type equations on the half-line with a prescribed flux at the boundary blowing up at a finite time, a result of independent interest.
Efficient Numerical Shadowing Global Error Estimation for High Dimensional Dissipative Systems
Authors: Collis Jon , Van Vleck Erik S. 
Published: March 2016

Abstract
Shadowing is a means of characterizing global errors in the numerical solution of initial value differential equations by allowing for small perturbations in the initial conditions. The method presented in this paper provides a technique for efficient estimation of the shadowing global error for systems that have a large number of exponentially decaying modes. The method is formulated for one-step methods and is applied to the spatial discretization of some dissipative PDEs.
Blow-up Results for Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term
Authors: Piccirillo Anna Maria , Toscano Luisa , Toscano Speranza 
Published: March 2016

Abstract
We obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problem

where λ > 0 is small, u0 ∈ Lloc(ℝN) with u0 ≥ 0, when

. For this purpose we use the method of “test function”.
Emergence of Waves in a Nonlinear Convection-Reaction-Diffusion Equation
Authors: Kamin Shoshana , Rosenau Philip 
Published: March 2016

Abstract
In this work we prove that for some class of initial data the solution of the Cauchy problem
ut = (um)xx + a(um)x + u(1 - um-1), x ∈ ℝ; t > 0
u(0; x) = u0(x), u0(x) ≥ 0
approaches the travelling solution, spreading either to the right or to the left, or two travelling waves moving in opposite directions.
Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions
Authors: Obersnel Franco , Omari Pierpaolo 
Published: March 2016

Abstract
An elementary approach, based on a systematic use of lower and upper solutions, is employed to detect the qualitative properties of solutions of first order scalar periodic ordinary differential equations. This study is carried out in the Carathéodory setting, avoiding any uniqueness assumption, in the future or in the past, for the Cauchy problem. Various classical and recent results are recovered and generalized.
Neural Architecture and Locomotion
Authors: Turner R.E.L. 
Published: March 2016

Abstract
Ascaris suum is a parasitic nematode that lives in pigs' intestines. It is a tempting subject for neurophysiologists in that it is 'simple', having only 300 neurons, about 80 of which are associated with locomotion. The muscular and neural structures are quite well understood, but the means by which they produce locomotion are not. In earlier work we developed a dynamic model for a single muscle cell; the model showed remarkably good correspondence with the voltage dynamics recorded in the laboratory. Here we use collections of model cells to represent dorsal and ventral muscle chains in the worm. The neuromuscular architecture in Ascaris is extremely complicated; we show, however, that by using suitable synaptic links between the model cells, we can create propagating waves of voltage variation that correspond to fictive motion.
Finite Speed of Propagation in Monostable Degenerate Reaction-Diffusion-Convection Equations
Authors: Malaguti Luisa , Marcelli Cristina 
Published: March 2016

AbstractWe study the existence and properties of travelling wave solutions of the Fisher-KPP reaction-diffusion-convection equation ut+ h(u)ux= [D(u)ux]x+ g(u), where the diffusivity D(u) is simply or doubly degenerate. Both the cases when Ḋ(0) and Ḋ(1) are possibly zero real values or infinity, are treated. We discuss the effects, due to the presence of a convective term, concerning the property of finite speed of propagation. Moreover, in the doubly degenerate case we show the appearance of new types of profiles and provide their classification according to sharp relations between the nonlinear terms of the model. An application is also presented, concerning the evolution of a bacterial colony.
Remarks on Nonlinear Elliptic Problems on Long Domains
Authors: Dancer E.N. 
Published: March 2016

Abstract
In this paper, we discuss the behaviour of solutions near a turning point for weakly nonlinear elliptic equations on long domains. We are looking for results independent of the domain length. In the process we obtain some local uniqueness and non-degeneracy results for homoclinic solutions on infinite strips.
Non-radial Maximizers For Functionals With Exponential Non-linearity in ℝ2
Authors: Calanchi Marta , Terraneo Elide 
Published: March 2016

Abstract
We consider the functional F : H1
0(B(0,1)) → ℝ

where α > 0,p > 0, 1 < γ ≤ 2, and B(0,1) is the unit ball in ℝ2. We prove that for any p > 0, 1 < γ < 2 and 0 < p < 4π, γ = 2 no maximizer of F(u) on the unit ball in H1
0 is radially symmetric provided that cu is large enough. This extends a result of Smets, Su and Willem concerning the existence of non-radial ground state solutions for the Rayleigh quotient related to the Hénon equation with Dirichlet boundary conditions.
Multiplicity of Positive Solutions For a Quasilinear Problem in IRN Via Penalization Method
Authors: Alves Claudianor O. , Figueiredo Giovany M. 
Published: March 2016

Abstract
The multiplicity and concentration of positive solutions are established for the equation −εpΔpu + V (z)|u|p-2u = f(u) in IRN, where V is a positive continuous function and f ∈ C1 is a function having subcritical and superlinear growth.
On the Least Action Principle – Hamiltonian Dynamics on Fixed Energy Levels in the Non-convex Case
Authors: Giambò Roberto , Giannoni Fabio , Piccione Paolo 
Published: March 2016

Abstract
We review the classical Principle of the Least Action in a general context where the Hamilton functionH is possibly non-convex. We show how the van Groesen [6] principle follows as a particular case where H is hyperregular and of homogeneous type. Homogeneous scalar field spacetimes in spherical symmetry are derived as an application.
Infinitely Many Solutions of Elliptic Problems With Perturbed Symmetries in Symmetric Domains
Authors: Clapp Mónica , Hernández-Martínez Eric 
Published: March 2016

Abstract
We study superlinear elliptic boundary value problems with perturbed symmetries in domains which are invariant under the action of a group G. We give conditions on the growth of the nonlinearity which guarantee the existence of infinitely many G-invariant solutions. These conditions improve those obtained by Bahri and Lions (1988) and Bolle, Ghoussoub and Tehrani (2000) if the domain contains a G-orbit of large enough dimension.
Existence of Multi-Bump Solutions For a Class of Quasilinear Problems
Authors: Alves Claudianor O. 
Published: March 2016

Abstract
Using variational methods we establish existence of multi-bump solutions for the following class of quasilinear problems
-Δpu + (λV(x) + Z(x))up-1 = f(u); u > 0 in ℝN

where Δpu is the p-Laplacian operator, 2 ≤ p < N, λ ∈ (0, ∞), f is a continuous function with subcritical growth and V,Z : ℝN → ℝ are continuous functions verifying some hypothesis.
On the Prescribed Paneitz Curvature Problem on the Standard Spheres
Authors: Abdelhedi Wael , Chtioui Hichem 
Published: March 2016

Abstract
In this paper, we study some fourth order conformal invariants on the standard n-spheres, n ≥ 5. Using topological arguments, we give a variety of classes of functions that can be realized as Paneitz curvature.
Large Solutions For a Class of Nonlinear Elliptic Equations With Gradient Terms
Authors: Leonori Tommaso 
Published: March 2016

Abstract
In this paper we prove the existence, in a suitable sense, of a large solution (a solution that blows-up at the boundary) for a class of nonlinear elliptic equations whose model is
-Δpu + u + u|▽u|q = f in Ω,
p > 1, p - 1 < q ≤ p and f(x) ∈ L1(Ω). The main tool in order to prove it relies on approximating the problem with a more regular one, prove local (i.e. independent from the behavior on the boundary) a priori estimates and local compactness for truncations in W1,p(Ω). Such scheme of the proof is also applied in order to prove the existence of a solution for equations of the type
-Δpu + u + u|▽u|q = f in ℝN,
where f(x) ∈ L1
loc(ℝN) without any condition at infinity. Moreover, the local summability of the solution depending on the local summability of the datum is studied.
Elliptic Obstacle Problems With Natural Growth on the Gradient and Singular Nonlinear Term
Authors: Arcoya David , Carmona José , Martínez-Aparicio Pedro J. 
Published: March 2016

Abstract
Given a bounded, open set Ω in ℝN (N ≥ 3), ψ∈ W1,p(Ω) (p > N) such that υ̸+ ∈ H0
1(Ω) ∩ L∞(Ω) and a suitable strictly positive (see (1.4)) function a ∈ Lq(Ω) with q > N/2, we prove the existence of positive solution w ∈ H0
1(Ω) of some variational inequality with a singular nonlinearity whose typical model is

where the set of test functions K1 consists of all functions υ ∈ H0
1(Ω) ∩ L∞(Ω) such that υ(x) ≥ ψ(x) a.e. x ∈ Ω and supp (υ - ψ+) ⊂⊂ Ω. Bigger classes of test functions are also studied. We also recover the case in which the variational inequality reduces to an equation.
Periodic Bounce Solutions of Hamiltonian Systems in Bounded Domains
Authors: Liu Yong , Jiang Mei-Yue 
Published: March 2016

Abstract
Periodic bounce solutions of the second order Hamiltonian system
−x″ = ∇V (x, t), x(t) ∈ Ω̅
is studied, where Ω ⊂ ℝN is a bounded domain diffeomorphic to the unit ball and V ∈ C2(Ω̅ × ℝ) is periodic in the time t.
Periodic Problem Involving Quasilinear Differential Operator and Weak Singularity
Authors: Cabada Alberto , Lomtatidze Alexander , Tvrdý Milan 
Published: March 2016

Abstract
We study the singular periodic boundary value problem of the form
(|u′|p−2 u′)′ = f(t, u), u(0) = u(T), u′(0) = u′(T),
where 1 < p < ∞ and f ∈ Car([0, T] × (0,∞)) can have a repulsive space singularity at x = 0. Contrary to previous results by Mawhin and Jebelean, Liu Bing and Rachůnková and Tvrdý, we need not assume any strong force conditions. Our main existence results rely on a new antimaximum principle for periodic quasilinear periodic problem, which has an independent meaning.
Classical and Non-Classical Sign-Changing Solutions of a One-Dimensional Autonomous Prescribed Curvature Equation
Authors: Obersnel Franco 
Published: March 2016

Abstract
We discuss existence and multiplicity of solutions of the one-dimensional autonomous prescribed curvature problem

, u(0) = 0, u(1) = 0,
depending on the behaviour at the origin and at infinity of the function f. We consider solutions that are possibly discontinuous at the points where they attain the value zero.
Dynamics of Generic Multidimensional Linear Differential Systems
Authors: Bessa Mário 
Published: March 2016

Abstract
We prove that there exists a residual subset R (with respect to the C0 topology) of d-dimensional linear differential systems based in a μ-invariant flow and with transition matrix evolving in GL(d,ℝ) such that if A ∈ R, then, for μ-a.e. point, the Oseledets splitting along the orbit is dominated (uniform projective hyperbolicity) or else the Lyapunov spectrum is trivial. Moreover, in the conservative setting, we obtain the dichotomy: dominated splitting versus zero Lyapunov exponents.
On Positive Solutions of Minimal Growth For Singular p-Laplacian With Potential Term
Authors: Pinchover Yehuda , Tintarev Kyril 
Published: March 2016

Abstract
Let Ω be a domain in ℝd, d ≥ 2, and 1 < p < ∞. Fix V ∈ L∞
loc(Ω). Consider the functional Q and its Gâteaux derivative Qʹ given by

It is assumed that Q ≥ 0 on C0
∞(Ω). In a previous paper [22] we discussed relations between the absence of weak coercivity of the functional Q on C0
∞(Ω) and the existence of a generalized ground state. In the present paper we study further relationships between functional-analytic properties of the functional Q and properties of positive solutions of the equation Qʹ(u) = 0.
Periodic Bifurcation For Semilinear Differential Equations With Lipschitzian Perturbations in Banach Spaces
Authors: Kamenskii Mikhail , Makarenkovy Oleg , Nistriz Paolo 
Published: March 2016

Abstract
Let A : D(A) → E, D(A) ⊂ E; be an infinitesimal generator either of an analytic compact semigroup or of a contractive C0-semigroup of linear operators acting in a Banach space E. In this paper we give both necessary and sufficient conditions for bifurcation of T- periodic solutions for the equation ẋ = Ax + f(t, x) + εg(t, x, ε) from a k-parameterized family of T-periodic solutions of the unperturbed equation corresponding to ε = 0. We show that by means of a suitable modification of the classical Mel’nikov approach we can construct a bifurcation function and to formulate the conditions for the existence of bifurcation in terms of the topological index of the bifurcation function. To do this, since the perturbation term g is only Lipschitzian we need to extend the classical Lyapunov- Schmidt reduction to the present nonsmooth case.
Multiplicity Result for Quasilinear Elliptic Problems with General Growth in the Gradient
Authors: Abdellaoui Boumediene 
Published: March 2016

Abstract
The main result of this work is to get the existence of infinitely many radial positive solutions to the problem
-Δpu = |▽u|q + λf(x) in Ω, u|aΩ = 0,
where Ω = B1(0) and f is a radial positive function. Since, in general when q ≠ p, a Hopf-Cole type change can not be used, we will consider just the existence and multiplicity of positive radial solutions. The main idea is to get a relation between radial positive solutions of the above equation and a suitable quasilinear family of problems with measures data that we will make precise later.
Symmetric And Nonsymmetric Solutions For a Class of Quasilinear Schrödinger Equations
Authors: Severo Uberlandio B. 
Published: March 2016

Abstract
We use the mountain-pass theorem combined with the principle of symmetric criticality to establish multiplicity of solutions for the class of quasilinear elliptic equations
-Δu + V(z)u - Δ(u2)u = h(u) in ℝN

where N ≥ 4, the potential V : ℝN → ℝ is positive and bounded away from zero and satisfies appropriate periodic and symmetric conditions. The nonlinear term h(u) has subcritical growth and satisfies a condition of the Ambrosetti-Rabinowitz type. Schrödinger equations of this type have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.
Existence of Solutions for a Semilinear Elliptic Equation in ℝN with Sign-changing Weight
Authors: Yang Jianfu , Yu Xiaohui 
Published: March 2016

Abstract
We study the existence of solutions for the semilinear elliptic equation

where 1 < p <

, Q(x) is a sign-changing function such that both the supports of Q+ and Q- may have infinite measure. We show that the problem has at least one solution.
Non-Radial Very Singular Similarity Solutions of Absorption-Diffusion Equations with Non-Homogeneous Potentials
Authors: Galaktionov V.A. 
Published: March 2016

Abstract
The semilinear heat equation with absorption and a power-type potential,
ut = Δu - |x|β|u|p-1u in ℝN × ℝ+, with p > 1, β > -2,
is considered. In the subcritical range

, this problem is shown to admit a finite set of self-similar very singular solutions (VSSs),

where f(y) has exponential decay at infinity and solves the semilinear elliptic equation

.
Some local bifurcation results are extended to the fourth-order equation
ut = -Δ2u - |x|β|u|p-1u, with p > 1, β > -4.
On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials
Authors: Ianni Isabella , Vaira Giusi 
Published: March 2016

Abstract
We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.
Sobolev Inequalities and Ellipticity of Planar Linear Hamiltonian Systems
Authors: Zhang Meirong 
Published: March 2016

Abstract
In this paper we will establish two different classes of ellipticity criteria, called the Lp criteria and the Lp-Lq criteria respectively, for planar linear Hamiltonian systems with periodic coefficients. The criteria are explicitly expressed using the Lp and Lq norms of coefficients and some known Sobolev constants. These results can be considered as the extensions of the famous Lyapunov stability criterion for Hill’s equations.
A Nonresonance Condition for Boundary Value Problems
Authors: Ward James Robert 
Published: March 2016

Abstract
We consider the boundary value problem
u″ + g(u)u = h(t, u, u′)
u(0) = 0, u(π) = 0
with g continuous, periodic, and positive and h continuous and bounded. It is shown that there is a solution if the mean value of g is not the square of an integer.
Existence, Asymptotic Behavior and Uniqueness for Large Solutions to Δu = eq(x)u
Authors: García-Melián Jorge , Sabina de Lis José C. , Rossi Julio D. 
Published: March 2016

Abstract
In this paper we consider existence, asymptotic behavior near the boundary and uniqueness for solutions to Δu = eq(x)u in a bounded smooth domain Ω with the boundary condition u(x) → + ∞ as dist(x, ∂Ω) → 0. The exponent q(x) is assumed to be a Hölder continuous function which is either positive on ∂Ω or is positive in a neighborhood of ∂Ω maybe vanishing on ∂Ω. When dealing with nonnegative exponents q we are allowing nonempty interior regions Ω0 ⊂ Ω where q vanishes. Changing sign exponents q will be also considered.
Multiple Solutions for Resonant Hemivariational Inequalities via Minimax Methods
Authors: Kyritsi Sophia Th. , O’ Regan Donal , Papageorgiou Nikolaos S. 
Published: March 2016

Abstract
In this paper we consider nonlinear Dirichlet problems driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequalities). We assume that the problem is resonant at infinity with respect to λ1 > 0 (the principal eigenvalue of the Dirichlet p-Lapalcian) from the right. Using minimax methods based on the nonsmooth critical point theory we prove an existence and a multiplicity theorem.
Evolution of Spacelike Hypersurfaces by Mean Curvature Minus External Force Field in Minkowski Space
Authors: Liu Yannan , Jian Huaiyu 
Published: March 2016

Abstract
We study the evolution of spacelike hypersurface moving by mean curvature minus an external force field in Minkowski space. It is shown that the flow will exist for all time if the initial spacelike surface has two compact spacelike barrier surfaces and the external force field satisfies a weak convexity condition.