On the relation between the weak Palais-Smale condition and coercivity given by Zhong

DOI10.1016/j.na.2007.01.071zbMath1354.49056OpenAlexW2001101160MaRDI QIDQ2479297

Tomonari Suzuki

Publication date: 26 March 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.01.071

zbMATH Keywords

coercivityPalais-Smale conditionEkeland's variational principle\(\tau \)-distanceZhong's variational principle

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Optimality conditions for problems in abstract spaces (49K27)

Related Items (7)

Redefinition of \(\tau\)-distance in metric spaces ⋮ Origin and evolution of the Palais-Smale condition in critical point theory ⋮ Meir-Keeler contractions of integral type are still Meir-Keeler contractions ⋮ Convergence of the sequence of successive approximations to a fixed point ⋮ Note on a general Palais-Smale condition ⋮ The strong Ekeland variational principle ⋮ Subrahmanyam's fixed point theorem

Cites Work

• A note on Palais-Smale condition and coercivity
• Viscosity solutions of Hamilton-Jacobi equations with unbounded nonlinear terms
• On Ekeland's variational principle and a minimax theorem
• Fixed point theorems and characterizations of metric completeness
• On Downing-Kirk's theorem.
• Generalized Caristi's fixed point theorems by Bae and others
• On the variational principle
• Several fixed point theorems concerning \(\tau\)-distance
• Nonconvex minimization problems
• Remarks on finding critical points
• Fixed Point Theorems for Mappings Satisfying Inwardness Conditions
• Contractive mappings, Kannan mappings and metric completeness
• A generalization of Ekerland's variational principle and application to the study of the relation between the weak P.S. condition and coercivity
• Generalized distance and existence theorems in complete metric spaces
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