Results 51 to 60 of about 2,493,959 (162)
Concentration–Compactness Principle to a Weighted Moser–Trudinger Inequality and Its Application
Journal of Mathematics, Volume 2025, Issue 1, 2025.We employ level‐set analysis of functions to establish a sharp concentration–compactness principle for the Moser–Trudinger inequality with power weights in R+2. Furthermore, we systematically prove the existence of ground state solutions to the associated nonlinear partial differential equation.
Yubo Ni, Agacik Zafer
wiley +1 more source
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
Failure of Plais-Smale condition and blow-up analysis for the critical exponent problem in R2 [PDF]
, 1997 Let Ω be a bounded smooth domain inR2. Letf:R→R be a smooth non-linearity behaving like exp{s2} ass→∞. LetF denote the primitive off. Consider the functionalJ:H01(Ω)→R given by J(u)=12∫Ω|∇u|2dx−∫ΩF(u)dx.
Adimurthi, ., Prashanth, S.
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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
MathematicsThis 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
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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
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
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 +2 more
wiley +1 more source
Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations [PDF]
, 2014 preprintIn this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold.
María del Mar González Nogueras +3 more
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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 +1 more
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