Results 21 to 30 of about 839,332 (169)

Existence of Solutions for Higher Order Bvp with Parameters via Critical Point Theory

Demonstratio Mathematica, 2015
This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.
Jurkiewicz Mariusz, Przeradzki Bogdan
doaj   +1 more source

Some Applications of Generalized Mountain Pass Lemma

, 2014
The Ghoussoub-Preiss's generalized Mountain Pass Lemma with Cerami-Palais-Smale type condition is a generalization of classical MPL of Ambrosetti-Rabinowitz, we apply it to study the existence of the periodic solutions with a given energy for some second order Hamiltonian systems with symmetrical and non-symmetrical potentials.
Li, Fengying, Li, Bingyu, Zhang, Shiqing
openaire   +2 more sources

Ground-State Solutions for a Class of N-Laplacian Equation with Critical Growth

Abstract and Applied Analysis, 2012
We investigate the existence of ground-state solutions for a class of N-Laplacian equation with critical growth in ℝN. Our proof is based on a suitable Trudinger-Moser inequality, Pohozaev-Pucci-Serrin identity manifold, and mountain pass lemma.
Guoqing Zhang, Jing Sun
doaj   +1 more source

Existence Results for a px-Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition

Journal of Applied Mathematics, 2013
We consider the existence and multiplicity of solutions for the px-Kirchhoff-type equations without Ambrosetti-Rabinowitz condition. Using the Mountain Pass Lemma, the Fountain Theorem, and its dual, the existence of solutions and infinitely many ...
Libo Wang, Minghe Pei
doaj   +1 more source

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds [PDF]

, 1995
Let M be a complete C1−Finsler manifold without boundary and f : M → R be a locally Lipschitz function. The classical proof of the well known deformation lemma can not be extended in this case because integral lines may not exist.
Tsachev, Tsvetomir, Krastanov, Mikhail, Ribarska, Nadezhda   +2 more
core   +1 more source

New Quantitative Deformation Lemma and New Mountain Pass Theorem

, 2014
In this paper, we obtain a new quantitative deformation Lemma so that we can obtain more critical points, especially for supinf critical value $c_1$, $x=φ^{-1}(c_1)$ is a new critical point. For $infmax$ critical value $c_2$, we can obtain two new critical points $x = 0$ (valley point) and $x = e$(peak point) ,comparing with Willem's variant of the ...
Ding, Liang, Zhang, Fode, Zhang, Shiqing
openaire   +2 more sources

L∞$L^\infty$ compactness of solutions of quasilinear problems and applications

Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.
Abstract For a (not necessarily smooth) bounded domain Ω$\Omega$ of RN$\mathbb {R}^N$, N⩾2$N \geqslant 2$ and a Carathéodory vector‐valued function a:Ω×RN→RN$a:\Omega \times \mathbb {R}^N \rightarrow \mathbb {R}^N$, we study the compactness of the inverse of the Leray–Lions operator A(u)=−div(a(x,∇u))$A(u)=-\text{div}(a(x, \nabla u))$, u∈W01,p(Ω)$u\in ...
D. Arcoya, M. C. M. Rezende, E. A. B. Silva   +2 more
wiley   +1 more source

Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces

Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 13324-13360, August 2026.
ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
wiley   +1 more source

Mountain pass techniques for some classes of nonvariational problems

, 2009
Existence results are presented for classical solutions to some nonvariational problems through a suitable approximation method of Mountain Pass critical ...
Matzeu, M, GIRARDI, Mario, MATZEU M., Mataloni, S, MATZEU, MICHELE, Girardi, M, MATALONI S   +6 more
core   +1 more source

A critical elliptic equation with a logarithmic type perturbation

Electronic Journal of Qualitative Theory of Differential Equations
In this note, we consider a critical elliptic equation perturbed by a logarithmic type subcritical term in $\mathbb{R}^4$, and investigate how the logarithmic term affects the existence of weak solutions to such a problem. Since the logarithmic term does
Haixia Li, Yuzhu Han
doaj   +1 more source