Results 51 to 60 of about 1,002 (168)

The Palais-Smale Condition on Contact Type Energy Levels for Convex Lagrangian Systems [PDF]

, 2003
Let L be a convex superlinear autonomous Lagrangian on a closed con- nected manifold N. We consider critical values of Lagrangians as de ned by R. Ma~ne in [23]. We de ne energy levels satisfying the Palais-Smale condition and we show that the critical
GONZALO ALBERTO CONTRERAS BARANDIARAN
core  

An estimate on the relative Morse index for strongly indefinite functionals

Electronic Journal of Differential Equations, 2001
We extend the Benci and Rabinowitz linking theorem to strongly indefinite functionals satisfying the Palais-Smale condition. More precisely, we show an upper estimate for a relative Morse index of critical points.
A. Abbondandolo, P. Felmer, J. Molina
doaj  

Multiplicity Results of Solutions to the Fractional p-Laplacian Problems of the Kirchhoff–Schrödinger–Hardy Type

Mathematics
This paper is devoted to establishing multiplicity results of nontrivial weak solutions to the fractional p-Laplacian equations of the Kirchhoff–Schrödinger type with Hardy potentials.
Yun-Ho Kim
doaj   +1 more source

Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems

Abstract and Applied Analysis, 2000
We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points.
Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou   +1 more
doaj   +1 more source

Planar Choquard equations with critical exponential reaction and Neumann boundary condition

Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.
Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat, Vicenţiu D. Rădulescu, K. Sreenadh   +2 more
wiley   +1 more source

A Variant of Clark\u27s Theorem and its Applications for Nonsmooth Functionals Without the Palais-Smale Condition

, 2017
By introducing a new notion of the genus with respect to the weak topology in Banach spaces, we prove a variant of Clark\u27s theorem for nonsmooth functionals without the Palais-Smale condition.
Zhi-Qiang Wang, Liu, Zhaoli, Shaowei Chen, Chen, Shaowei, Zhaoli Liu, Wang, Zhi-Qiang   +5 more
core   +1 more source

Half-Reeb components, Palais-Smale condition and global injectivity of local diffeomorphisms in R3 [PDF]

, 2014
Let F = (F1, F2, F3): R3 → R3 be a C∞ local diffeomorphism. We prove that each of the following conditions are sufficient to the global injectivity of F: A) The foliations FFi made up by the connected components of the level surfaces Fi = constant ...
Braun, Francisco, Venato-Santos, Jean
core   +1 more source

Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator

Electronic Journal of Differential Equations, 2013
In this article, we study superlinear Dirichlet problems involving the p(x)-Laplace operator without using the Ambrosetti-Rabinowitz's superquadraticity condition.
Mustafa Avci
doaj  

Least energy solutions for a class of (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problems in RN$\mathbb {R}^{N}$ with general nonlinearities

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We examine the following (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problem: −M1∥∇u∥Lp1(RN)p1Δp1u−M2∥∇u∥Lp2(RN)p2Δp2u=g(u)inRN,u∈W1,p1(RN)∩W1,p2(RN),$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{ll}-M_{1}\left(\Vert \nabla u\Vert ^{p_{1}}_{L^{p_{1}}(\mathbb {R}^{N})}\right)\Delta _{p_{1}}u-M_{2}\left(\Vert \nabla u\Vert ^{p_{2 ...
Vincenzo Ambrosio
wiley   +1 more source

Generalized noncooperative Schrödinger–Kirchhoff–type systems in RN$\mathbb {R}^N$

Mathematische Nachrichten, Volume 297, Issue 6, Page 2092-2121, June 2024.
Abstract We consider a class of noncooperative Schrödinger–Kirchhof–type system, which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the existence of infinitely many solutions for the problem by using the limit index theory, a version of concentration ...
Nabil Chems Eddine, Dušan D. Repovš
wiley   +1 more source