Results 51 to 60 of about 3,788 (155)

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

Solutions to a nonlinear Schr\"odinger equation with periodic potential and zero on the boundary of the spectrum [PDF]

, 2014
We study the following nonlinear Schr\"odinger equation $$-\Delta u + V(x) u = g(x,u),$$ where V and g are periodic in x. We assume that 0 is a right boundary point of the essential spectrum of $-\Delta+V$.
Mederski, Jarosław
core   +2 more sources

A mountain pass theorem without Palais–Smale condition

Comptes Rendus. Mathématique, 2005
Given a Hilbert space (H,〈⋅,⋅〉), Λ an interval of R and J∈C2(H,R) whose gradient ∇J:H→H is a compact mapping, we consider a family of functionals of the type: I(λ,u)=〈u,u〉−λJ(u),(λ,u)∈Λ×H. Without further compactness assumptions, we present a deformation lemma to detect critical points. In particular, if I(λ¯,⋅) has a ‘mountain pass structure’ for some
openaire   +2 more sources

A note on Palais-Smale condition and coercivity

Differential and Integral Equations, 1990
It has been observed [the second author, An existence theorem on multiple critical points and its applications in nonlinear P.D.E., in Differential geometry and differential equations, Proc. Symp., Changchun/China 1982, 479-483 (1986); the third author, An introduction to critical point theory (1988)] that, for a \(C^ 1\) function \(\varphi\) bounded ...
Čaklović, L., Li, Shu Jie, Willem, M.
openaire   +3 more sources

Existence and Nonexistence of Periodic Solutions for a Class of Fourth‐Order Partial Difference Equations

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we investigate multiplicity, existence, and nonexistence of periodic solutions to a fourth‐order partial difference equation via linking theorem and saddle point theorem. Our obtained results significantly generalize and improve some existing ones.
Dan Li, Yuhua Long, Ji Gao
wiley   +1 more source

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  

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

The concentration-compactness principle for variable exponent spaces and applications [PDF]

, 2009
In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to the variable exponent case.
Bonder, J. Fernandez, Silva, A.
core   +3 more sources

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

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