A generalized mountain pass lemma with a closed subset for locally Lipschitz functionals

DOI10.1080/00036811.2021.1903441zbMath1502.49005arXiv2102.04387OpenAlexW3135952749WikidataQ124979666 ScholiaQ124979666MaRDI QIDQ5037935

Zhang, Shiqing, Fengying Li, Bingyu Li

Publication date: 29 September 2022

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.04387

zbMATH Keywords

locally Lipschitz functionalsEkeland's variational principleClarke's generalized gradientgeneralized mountain pass lemmaMountain pass lemma of Ambrosetti-Rabinowitz

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued maps in general topology (54C60) Variational methods applied to PDEs (35A15) Existence of solutions for minimax problems (49J35) Variational principles in infinite-dimensional spaces (58E30)

Cites Work

• Origin and evolution of the Palais-Smale condition in critical point theory
• A general mountain pass principle for locating and classifying critical points
• A min-max principle for non-differentiable functions with a weak compactness condition
• Critical points of non-smooth functions with a weak compactness condition
• Extensions of the mountain pass theorem
• A mountain pass theorem
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Periodic solutions of singular Lagrangian systems
• On the variational principle
• Applied functional analysis. Applications to mathematical physics. Vol. 1
• Dual variational methods in critical point theory and applications
• Existence and classification of critical points for nondifferentiable functions
• Mountain Passes and Saddle Points
• A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain-Pass Theorem
• Optimization and nonsmooth analysis
• Ekeland's variational principle and the mountain pass lemma
• The Structure of the Critical Set in the Mountain Pass Theorem
• A Min-max Principle with a Relaxed Boundary Condition
• Beyond the Mountain Pass: Some Applications
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