bluuebunny/crossref_metadata_2025_split huggingface dataset:
Multiple Solutions for the p(x)− Laplace Operator with Critical Growth
Authors: Silva Analia 
Published: March 2016

Abstract
The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δp(x)u = |u|q(x)−2u + λ f (x, u) in a smooth bounded domain Ω of RN with homogeneous Dirichlet boundary conditions on ∂Ω. We assume that {q(x) = p∗(x)} ≠ ø, where p∗(x) = Np(x)/(N − p(x)) is the critical Sobolev exponent for variable exponents and Δp(x)u = div(|∇u|p(x)−2∇u) is the p(x)−laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces.
Periodic Solutions of Systems with Singularities of Repulsive Type
Authors: Amster Pablo , Maurette Manuel 
Published: March 2016

Abstract
Motivated by the classical Coulomb central motion model, we study the existence of T-periodic solutions for the nonlinear second order system of singular ordinary differential equations u′′ + g(u) = p(t). Using topological degree methods, we prove that when the nonlinearity g : ℝN\{0} →ℝN is continuous, repulsive at the origin and bounded at infinity, if an appropriate Nirenberg type condition holds then either the problem has a classical solution, or else there exists a family of solutions of perturbed problems that converge uniformly and weakly in H1 to some limit function u. Furthermore, under appropriate conditions we prove that u is a classical solution.
A Note on the Complete Rotational Invariance of Biradial Solutions to Semilinear Elliptic Equations
Authors: Abatangelo L. , Terracini S. 
Published: March 2016

Abstract
We investigate symmetry properties of solutions to equations of the form
-Δu =

+ f(|x|, u)
in ℝN for N ≥ 4, with at most critical nonlinearities. By using geometric arguments, we prove that solutions with low Morse index (namely 0 or 1) and which are biradial (i.e. are invariant under the action of a toric group of rotations), are in fact completely radial. A similar result holds for the semilinear Laplace-Beltrami equations on the sphere. Furthermore, we show that the condition on the Morse index is sharp. Finally we apply the result in order to estimate best constants of Sobolev type inequalities with different symmetry constraints.
Equivalence of Some Multi-Valued Elliptic Variational Inequalities and Variational-Hemivariational Inequalities
Authors: Carl Siegfried 
Published: March 2016

Abstract
First, we prove existence and comparison results for multi-valued elliptic variational inequalities involving Clarke’s generalized gradient of some locally Lipschitz functions as multi-valued term. Only by applying the definition of Clarke’s gradient it is well known that any solution of such a multi-valued elliptic variational inequality is also a solution of a corresponding variational-hemivariational inequality. The reverse is known to be true if the locally Lipschitz functions are regular in the sense of Clarke. Without imposing this kind of regularity the equivalence of the two problems under consideration is not clear at all. The main goal of this paper is to show that the equivalence still holds true without any additional regularity, which will fill a gap in the literature. Existence and comparison results for both multi-valued variational inequalities and variational-hemivariational inequalities are the main tools in the proof of the equivalence of these problems.
Stability and the Growth of the Number of Closed Characteristics on Compact Convex Hypersurfaces
Authors: Liu Hui 
Published: March 2016

Abstract
In this paper, we study relationship between the stability and the growth of the number of closed characteristics on compact convex hypersurfaces in ℝ2n, and also the stability of closed characteristics on compact convex hypersurfaces in ℝ2n under some pinching conditions.
A Variational Approach to a Nonlocal Elliptic Problem with Sign-Changing Nonlinearity
Authors: Corrêa Francisco Julio S.A. , Delgado Manuel , Suárez Antonio 
Published: March 2016

Abstract
In this paper we are concerned with the nonlocal elliptic problem

where Ω ⊂ℝN is a bounded smooth domain, f, g : ℝ →ℝ are given functions and p is a fixed real number. We use variational methods to prove multiplicity results.
On the Existence of Three Nontrivial Solutions for Periodic Problems Driven by the Scalar p-Laplacian
Authors: Papageorgiou Nikolaos S. , Papalini Francesca 
Published: March 2016

Abstract
We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential function. First we establish an alternative minimax expression for the first nonzero eigenvalue for the negative periodic scalar p-Laplacian and then using it we prove the existence of three nontrivial solutions, two of which have constant sign. Our approach is variational, based on the nonsmooth critical point theory.
Heteroclinic Solutions to Asymptotically Autonomous Equations via Continuation Methods
Authors: Gavioli Andrea 
Published: March 2016

Abstract
By means of a continuation argument, we prove the existence of at least one increasing heteroclinic solution to a scalar equation of the kind ẍ = a(t)V′(x), where V is a non-negative double well potential, and a(t) is a positive, measurable coefficient, which is definitively monotone with respect to |t|, converges to l as |t| diverges and fulfils one of the two following assumptions: a(t) ≥ l everywhere, or a(t) − l converges to 0, as |t| → +∞, more slowly than a suitable exponential term.
Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms
Authors: Abdellaoui Boumediene , Dall’Aglio Andrea , Peral Ireneo , Léon Sergio Segura de 
Published: March 2016

Abstract
In the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum:

where 1 < p < N, Ω is a bounded open subset of ℝN (N ≥ 2), Δpu = div(|∇u|p−2∇u) is the so called p-Laplacian operator,

sign s ., ϕ(ν0) ∈ L1(Ω), μ is a finite Radon measure and f ∈ L∞(Ω×(0, T)) for every T > 0. Then we apply this existence result to show wild nonuniqueness for a connected nonlinear parabolic problem having a gradient term with natural growth.
Smoothness of Asymptotic Phase Revisited
Authors: Battelli Flaviano , Palmer Kenneth J. 
Published: March 2016

Abstract
It is well-known that solutions on the stable manifold of a hyperbolic periodic solution of an autonomous system of ordinary differential equations have an asymptotic phase which has the same order of smoothness as the vector field. In this paper we show if the system depends on a parameter that, in general, the asymptotic phase loses one order of smoothness in the parameter.
Existence and Uniqueness of Solutions for a Class of p-Laplace Equations on a Ball
Authors: Korman Philip 
Published: March 2016

Abstract
For a class of equations generalizing the model case
Δpu − a(r)up−1 + b(r)uq = 0 in B, u = 0 on∂B,
where B is the unit ball in Rn, n ≥ 1, r = |x|, p, q > 1, and Δp denotes the p-Laplace operator, we give conditions for the existence and uniqueness of positive solution. In case n = 1, we give a more general result.
A Biharmonic Equation in ℜ4 Involving Nonlinearities with Subcritical Exponential Growth
Authors: Sani Federica 
Published: March 2016

Abstract
In this paper we consider a biharmonic equation of the form Δ2u+V(x)u = f (u) in the whole four-dimensional space ℜ4. Assuming that the potential V satisfies some symmetry conditions and is bounded away from zero and that the nonlinearity f is odd and has subcritical exponential growth (in the sense of an Adams’ type inequality), we prove a multiplicity result. More precisely we prove the existence of infinitely many nonradial sign-changing solutions and infinitely many radial solutions in H2(ℜ4). The main difficulty is the lack of compactness due to the unboundedness of the domain ℜ4 and in this respect the symmetries of the problem play an important role.
On the Convergence of Solutions of Globally Modified Navier-Stokes Equations with Delays to Solutions of Navier-Stokes Equations with Delays
Authors: Marín-Rubio Pedro , Real José , Márquez-Durán Antonio M. 
Published: March 2016

Abstract
We prove that under suitable assumptions, from a sequence of solutions of Globally Modified Navier-Stokes equations with delays we can extract a subsequence which converges in an adequate sense to a weak solution of a three-dimensional Navier-Stokes equation with delays. An additional case with a family of different delays involved in the approximating problems is also discussed.
Global Bifurcations of Critical Orbits via Equivariant Conley Index
Authors: Rybicki Sławomir 
Published: March 2016

Abstract
Let V be a finite-dimensional representation of a compact connected Lie group G and let ϕ : V × [λ1, λ2] → ℝ be a family of G-invariant potentials of the class C2 such that ∇vϕ(0, λ) = 0 for every λ ∈ [λ1, λ2], where ∇vϕ is the gradient of ϕ with respect to the first coordinate. Denote by V′i a direct sum of eigenspaces of the isomorphism ∇v
2 ϕ(0, λi) corresponding to positive eigenvalues, i = 1, 2. We have proved that if dimV′1 ≧ dimV′2 and the representation V′1 is not equivalent (as a linear representation of G) to the representation V′2 ⊕ ℝ[2k], k ∈ {0} ∪ ℕ (where ℝ[2k] is a 2k-dimensional trivial representation of G), then there is a global bifurcation of G-orbits of non-zero solutions of problem ∇vϕ(v, λ) = 0 from the interval {0} × [λ1, λ2]. We have proved that a global bifurcation and symmetrybreaking of solutions phenomenon occurs simultaneously for elliptic differential equations considered by Smoller and Wasserman in [25], which improves results of [25].
Blow up Points and the Morse Indices of Solutions to the Liouville Equation in Two-Dimension
Authors: Takahashi Futoshi 
Published: March 2016

Abstract
We consider the Liouville equation
−Δu = λeu in Ω, u =0 on∂Ω,
on a smooth bounded domain Ω in ℝ2, where λ > 0 is a parameter. Let {un} be an m-point blowing up solution sequence of the problem for λ = λn ↓ 0, which satisfies

for m ∈ℕ. We prove that the number of blow up points m is less than or equal to the Morse index of un for n sufficiently large.
As a corollary, we show that if a solution un of Morse index one has the property that

, then the number of blow up points of the sequence is exactly one. Note that in the last result, we do not need any geometrical assumption such as the convexity of the domain.
Nonexistence Results of Sign-changing solutions for a Supercritical Problem of the Scalar Curvature Type
Authors: Ould Bouh Kamal 
Published: March 2016

Abstract
This paper is devoted to the study of the nonlinear elliptic problem with supercritical critical exponent (Pε) : −Δu = K|u|4/(n−2)+εu in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 3, K is a C3 positive function and ε is a positive real parameter. We show first that in dimension 3, for ε small, (Pε) has no sign-changing solutions with low energy which blow up at two points. For n ≥ 4, we prove that there are no sign-changing solutions which blow up at two nearby points. We also show that (Pε) has no bubble-tower sign-changing solutions.
Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane
Authors: Fonda Alessandro , Toader Rodica 
Published: March 2016

Abstract
By the use of a generalized version of the Poincaré-Birkhoff fixed point theorem, we prove the existence of at least two periodic solutions for a class of Hamiltonian systems in the plane, having in mind the forced pendulum equation as a particular case. Our approach is closely related to the one used by Franks in [15], but the proof remains at a more elementary level.
Asymptotic Approach to Inverse Bifurcation for Nonlinear Sturm-Liouville Problems
Authors: Shibata Tetsutaro 
Published: March 2016

Abstract
We consider the nonlinear inverse bifurcation problem
−u′′(t) + f (u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0,
where λ > 0 is a positive parameter, and the nonlinear term f (u) is unknown. We show that, if the asymptotic behavior of the Lq-bifurcation curve λ = λq(α) (1 ≤ q < ∞) of the positive solutions is understood well, then we are able to obtain f (u) and to characterize the asymptotic behavior of f(u) as u → ∞.
Dual Spaces of Weighted Multi-Parameter Hardy Spaces Associated with the Zygmund Dilation
Authors: Han Xiaolong , Lu Guozhen , Xiao Yayuan 
Published: March 2016

Abstract
In this paper, we apply the discrete Littlewood-Paley-Stein analysis to prove the duality theorem of weighted multi-parameter Hardy spaces associated with Zygmund dilations, i.e., (HpZ (ω))∗ = CMOZ
p (ω) for 0 < p ≤ 1. Our theorems extend the HZ
p - CMOZ
p duality theorems established in [13] (see also [12]) for non-weighted multi-parameter Hardy spaces associated with the Zygmund dilation.
On Variational Inequalities Driven by Elliptic Operators Not in Divergence Form
Authors: Matzeu Michele , Servadei Raffaella 
Published: March 2016

Abstract
In this paper we study semilinear variational inequalities driven by an elliptic operator not in divergence form modeled by

where Ω is a bounded domain of RN, N ≥ 3, with smooth boundary, A is the elliptic operator, not in divergence form, given by

Here aij, ai , i,j = 1,...,N , and a0 satisfy suitable regularity conditions, while 1 < s < 4/(N − 2) and the obstacle ψ is a function sufficiently smooth. Even if this problem is not variational in nature, we will prove the existence of non-trivial non-negative solutions for it, performing a variational approach combined with a penalization technique. This kind of approach seems to be new for problems of this type. We also prove a C1,α-regularity result for the solutions of our problem.
Solitary Waves and Vortices in Non-Abelian Gauge Theories with Matter
Authors: Benci Vieri , Bonanno Claudio 
Published: March 2016

Abstract
We consider a non-Abelian gauge theory in ℝ4 equipped with the Minkowski metric, which provides a model for the interaction between a bosonic matter field and a gauge field with gauge group S U(2). We prove the existence of solitary waves which are related to those found for the Klein-Gordon-Maxwell equations.
Bifurcation Analysis at a Singular Soliton State in Fiber Couplers
Authors: Buffoni Boris 
Published: March 2016

Abstract
The system

describes pulses in nonlinear fiber couplers. It has the family (U1+λ, -U1+λ), -1 < λ < ∞, of soliton states (that is, homoclinic solutions to the origin), where

For λ ≥ 1, the equilibrium (0, 0) is not hyperbolic and therefore the soliton state (U1+λ, −U1+λ) can be qualified as “singular”. In N. Akhmediev and A. Ankiewicz [1], it is observed numerically that a branch of homoclinic solutions bifurcates subcritically at λ = 1 from the family (U1+λ, −U1+λ). The aim of the present paper is to give a rigorous proof of the existence of this bifurcation, as desired in A. Ambrosetti and D. Arcoya [3]. A particular feature of the present problem is that the linearized system at (U2, −U2) has a non-constant bounded solution that does not vanish at infinity. Hence the bifurcating homoclinic solutions have a transient “spatial” region where they are well described with the help of this bounded function. Moreover the decay to 0 is governed by two different scales, the larger one originating from the singular aspect of (U2, −U2). The existence proof developed here relies on the “broken geodesic” technique to match the inside transient region with the outside region.
Counterexamples to C2 Boundary Estimates for a Fully Nonlinear Yamabe Problem on Manifolds with Boundary
Authors: Li YanYan , Nguyen Luc 
Published: March 2016

Abstract
On closed manifolds, gradient and Hessian a priori estimates for fully nonlinear Yamabe problems are known to hold. On manifolds with boundary, gradient estimates are known to hold, while Hessian estimates hold if the prescribed mean curvature is positive. Examples are given here which show that Hessian estimates can fail when the mean curvature is negative.
ω-Index Theory and Linear Stability of Elliptic Lagrangian Solutions of the Classical Three-Body Problem
Authors: Long Yiming 
Published: March 2016

Abstract
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter β = 27(m1m2 + m2m3 + m3m1)/(m1 + m2 + m3)2 ∈ [0, 9] and the eccentricity ℯ ∈ [0, 1). We are not aware of any existing analytical method which relates the linear stability of these solutions to these two parameters directly in the full rectangle [0, 9] × [0, 1), besides perturbation methods for ℯ > 0 small enough, blow-up techniques for e sufficiently close to 1, and numerical studies. In the recent paper [5], X. Hu, S. Sun and the author introduced a new rigorous analytical method to study the linear stability of these solutions in terms of the two parameters in the full (β, ℯ) range [0, 9] × [0, 1) via the ω-index theory of symplectic paths for ω belonging to the unit circle of the complex plane, and the theory of linear operators. This is an expository article on [5]. In Section 1 of this paper we give a brief review on the history of this stability problem, and describe recent results obtained in [5]. Then in Section 2, after reviewing the ω-index theory in [15], the ω-index decreasing property of the elliptic Lagragian solutions in β for fixed ℯ ∈ [0, 1) proved in [5] is introduced, then the existence of three curves located from left to right in the parameter rectangle [0, 9] × [0, 1) is explained. Among these three curves, two are precisely the −1 degeneracy curves and the third one is the left boundary curve of the hyperbolic subregion in [0, 9] × [0, 1). Then in Section 3, it is explained why the linear stability pattern of such an elliptic Lagrangian solution qβ,ℯ changes if and only if the parameter (β, ℯ) passes through one of these three curves. Some open problems on related topics are suggested at the end of this paper.
Pairs of Nodal Solutions for a Class of Nonlinear Problems with One-sided Growth Conditions
Authors: Boscaggin Alberto , Zanolin Fabio 
Published: March 2016

Abstract
Boundary value problems of Sturm-Liouville and periodic type for the second order nonlinear ODE uʺ + λf(t, u) = 0 are considered. Multiplicity results are obtained, for λ positive and large, under suitable growth restrictions on f(t, u) of superlinear type at u = 0 and of sublinear type at u = ∞. Only one-sided growth conditions are required. Applications are given to the equation uʺ + λq(t)f(u) = 0, allowing also a weight function q(t) of nonconstant sign.
Bifurcation Results of Positive Solutions for an Indefinite Nonlinear Elliptic System II
Authors: Tian Rushun , Wang Zhi-Qiang 
Published: March 2016

Abstract
We study local and global bifurcations of the following elliptic system

where the constant a is greater than the principal eigenvalue of (-Δ,Ω), and Ω ⊂ ℝN is a bounded smooth domain (N ≤ 3). The parameters μ1,μ2 are real numbers. We identify some intervals of β in which there exist finitely many bifurcation points with respect to a trivial solution branch. In particular, when N = 1 or Ω is radial, every bifurcation branch exists globally and is characterized by a nodal property for the difference of the two components of the solutions.
N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition
Authors: Lam Nguyen , Lu Guozhen 
Published: March 2016

Abstract
Let Ω be a bounded domain in ℝN. In this paper, we consider the following nonlinear elliptic equation of N-Laplacian type:

when f is of subcritical or critical exponential growth. This nonlinearity is motivated by the Moser-Trudinger inequality. In fact, we will prove the existence of a nontrivial nonnegative solution to (0.1) without the Ambrosetti-Rabinowitz (AR) condition. Earlier works in the literature on the existence of nontrivial solutions to N−Laplacian in ℝN when the nonlinear term f has the exponential growth only deal with the case when f satisfies the (AR) condition. Our approach is based on a suitable version of the Mountain Pass Theorem introduced by G. Cerami [9, 10, 21]. Examples of f and comparison with earlier assumptions in the literature are given.
Morse Decomposition of Attractors for Non-autonomous Dynamical Systems
Authors: Caraballo Tomás , Jara Juan C. , Langa José A. , Liu Zhenxin 
Published: March 2016

Abstract
A Morse decomposition of a global attractor describes its internal dynamics, i.e., the dynamics on invariant compact sets in the attractor and the connections between them. When we deal with non-autonomous dynamical systems, the concept of pullback attractor for the associated skew-product flow appears as a powerful tool to analyze the asymptotic behaviour of these systems. In this paper we develop a Morse decomposition theory for pullback attractors of non-autonomous dynamical systems in Banach spaces with compact base space which, in particular, defines a (non-autonomous) Lyapunov functional on the attractor describing a decaying energy level on the evolution of trajectories.
Weak Solutions and Energy Estimates for a Class of Nonlinear Elliptic Neumann Problems
Authors: Bonanno Gabriele , Molica Bisci Giovanni , Rădulescu Vicenţiu D. 
Published: March 2016

Abstract
We establish existence results and energy estimates of solutions for a homogeneous Neumann problem involving the p-Laplace operator. The case of large dimensions, corresponding to the lack of compactness of W1,p(Ω) in C0(Ω̅) is also considered. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established, without requiring any asymptotic condition at zero or at infinity of the nonlinear term. In the case of (p − 1)-sublinear terms at the origin, we deduce the existence of solutions for small positive values of the parameter and we obtain that the corresponding solutions have smaller and smaller energies as the parameter goes to zero. Finally, a multiplicity result is obtained and concrete examples of applications are provided. A basic ingredient in our arguments is a recent local minimum theorem for differentiable functionals.
Global Attractors for p-Laplacian Equations with Dynamic Flux Boundary Conditions
Authors: You Bo , Zhong Chengkui 
Published: March 2016

Abstract
This paper studies the long-time behavior of solutions for p-Laplacian equations with a polynomial growth nonlinearity of arbitrary order and dynamic flux boundary conditions in d-dimensional bounded smooth domains. We first prove the existence of global attractors in L2(Ω)×L2(Γ) and Lq(Ω)×Lq(Γ) for the p-Laplacian evolution equations subject to dynamic nonlinear boundary conditions by using the Sobolev compactness embedding theory, and then the existence of (L2(Ω) × L2(Γ), L2(q−1)(Ω) × L2(q−1)(Γ))-global attractor is obtained by asymptotical regularity method. Finally, we prove the existence of global attractor in W1,p(Ω) ∩ Lq(Ω)) × Lq(Γ) by asymptotic a priori estimate.
Local Inversion of Planar Maps with Nice Nondifferentiability Structure
Authors: Poggiolini Laura , Spadini Marco 
Published: March 2016

Abstract
When the plane is pie-sliced in n ≤ 4 parts (with nonempty interior and common vertex at the origin) our main result provides sufficient conditions for any map L, that is continuous and piecewise linear relatively to this slicing, to be invertible. This result cannot be plainly extended to a greater number of slices. Also, some examples show that the assumptions cannot be relaxed too much. Our result is proved by a combination of linear algebra and topological arguments.