A Bounded Mountain Pass Lemma Without the (PS) Condition and Applications
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Publication:4018460
DOI10.2307/2154135zbMath0757.35026OpenAlexW4231534994WikidataQ124988249 ScholiaQ124988249MaRDI QIDQ4018460
Publication date: 16 January 1993
Full work available at URL: https://doi.org/10.2307/2154135
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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