A Bounded Mountain Pass Lemma Without the (PS) Condition and Applications

DOI10.2307/2154135zbMath0757.35026OpenAlexW4231534994WikidataQ124988249 ScholiaQ124988249MaRDI QIDQ4018460

Schechter, Martin

Publication date: 16 January 1993

Full work available at URL: https://doi.org/10.2307/2154135

zbMATH Keywords

semilinear Dirichlet problemsno Palais-Smale condition requirement

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Equations involving nonlinear operators (general) (47J05) 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 (13)

Linking-type results in nonsmooth critical point theory and applications ⋮ Multiple solutions for semilinear elliptic problems ⋮ Superlinear elliptic boundary value problems ⋮ Eigenvalues for semilinear boundary value problems ⋮ The Hampwile theorem for nonlinear eigenvalues ⋮ Double linking theorem and multiple solutions. ⋮ Critical point theorems in cones and multiple positive solutions of elliptic problems ⋮ The Leray-Schauder boundary condition in critical point theory ⋮ A compression type mountain pass theorem in conical shells ⋮ Multiple positive standing wave solutions for Schrödinger equations with oscillating state-dependent potentials ⋮ The mountain pass alternative ⋮ Asymptotically linear elliptic boundary value problems ⋮ A Schechter type critical point result in annular conical domains of a Banach space and applications

Cites Work

• The Hampwile theorem for nonlinear eigenvalues
• Some remarks on the number of solutions of some nonlinear elliptic problems
• A mountain pass theorem
• Coincidence degree, and nonlinear differential equations
• On the solvability of semilinear gradient operator equations
• On an elliptic boundary value problem at double resonance
• Dual variational methods in critical point theory and applications
• Lusternik-Schnirelman theory on Banach manifolds
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues
• Multiplicity results for a semilinear boundary value problem with the nonlinearity crossing higher Eigenvalues
• Multiple Nontrivial Solutions of Resonant and Nonresonant Asymptotically Linear Problems
• Non-trivial solutions of elliptic equations at resonance
• Variational and topological methods in nonlinear problems
• Generalizing the Lusternik‐Schnirelman theory of critical points
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