Results 1 to 10 of about 729 (179)

Relations between the mountain pass theorem and local minima

Advances in Nonlinear Analysis, 2012
Existence results of two critical points for functionals unbounded from below are established after pointing out a characterization of the mountain pass geometry. Applications to elliptic Dirichlet problems are then presented.
Bonanno Gabriele
doaj   +4 more sources

A mountain pass theorem

Journal of Differential Equations, 1985
In this paper we establish a new version of the well-known theorem of Ambrosetti and Rabinowitz on the existence of critical points for functionals \(I: X\to {\mathbb{R}}\) of class \(C^ 1\) on a real Banach space X. As usual, a compactness condition of Palais-Smale type is assumed throughout, including a version particularly suited to the periodic ...
PUCCI, Patrizia, J. SERRIN
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Extensions of the mountain pass theorem

Journal of Functional Analysis, 1984
The paper contains a number of extensions of the mountain pass lemma of \textit{A. Ambrosetti} and \textit{P. H. Rabinowitz} [(*) ibid. 14, 349-381 (1973; Zbl 0273.49063)]. The lemma gives sufficient conditions for the existence of critical points of continuously Fréchet differentiable functionals \(I: X\to {\mathbb{R}}\) on a real Banach space X.
PUCCI, Patrizia, J. SERRIN
openaire   +5 more sources

Multiple solutions for a quasilinear Choquard equation with critical nonlinearity

Open Mathematics, 2021
In the present work, we are concerned with the multiple solutions for quasilinear Choquard equation with critical nonlinearity in RN{{\mathbb{R}}}^{N}.
Li Rui, Song Yueqiang
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Image restoration via Picard's and Mountain-pass Theorems

Electronic Research Archive, 2022
<abstract><p>In this work, we present existence results for some problems which arise in image processing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point.</p></abstract>
Souad Ayadi, Özgür Ege
openaire   +2 more sources

On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent

Journal of Function Spaces, 2022
In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
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On mountain pass theorem and its application to periodic solutions of some nonlinear discrete systems

Advances in Difference Equations, 2019
In this paper, we prove a new quantitative deformation lemma, and then gain a new mountain pass theorem in Hilbert spaces. By using the new mountain pass theorem, we obtain the new existence of two nontrivial periodic solutions for a class of nonlinear ...
Liang Ding, Jinlong Wei, Shiqing Zhang
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Existence and multiplications of solutions for a class of equation with a non-smooth potential [PDF]

Journal of Hyperstructures, 2015
This paper deals with the existence and multiplicity of solutions for a class of nonlocal p−Kirchhoff problem. Using the mountain pass theorem and fountain theorem, we establish the existence of at least one solution and infinitely many solutions for a ...
Fariba Fattahi, M. Alimohammady
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GENERAL QUASILINEAR PROBLEMS INVOLVING \(p(x)\)-LAPLACIAN WITH ROBIN BOUNDARY CONDITION

Ural Mathematical Journal, 2020
This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving \(p(x)\)-Laplace type equation, namely $$ \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u ...
Hassan Belaouidel, Anass Ourraoui, Najib Tsouli   +2 more
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Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Damped Vibration Problems with Impulsive Effects

Abstract and Applied Analysis, 2014
This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects.
Qiongfen Zhang
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