Multiple solutions for indefinite functionals and applications to asymptotically linear problems

DOI10.1007/BF02107664zbMath0685.58008MaRDI QIDQ4735802

No author found.

Publication date: 1989

Published in: Acta Mathematica Sinica (Search for Journal in Brave)

zbMATH Keywords

orbitsHamiltonian systemscritical pointmultiple critical pointscriticalMorse theory in Hilbert spaces

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (22)

Solutions of elliptic problems with nonlinearities of linear growth ⋮ DIRICHLET PROBLEM OF ELLIPTIC EQUATIONS WITH STRONG RESONANCES ⋮ Symmetries, morse polynomials and applications to bifurcation problems ⋮ Infinitely many periodic solutions for asymptotically linear Hamiltonian systems ⋮ Nontrivial solutions of elliptic systems with nonlinearities may not have asymptotic limits ⋮ Infinitely many solutions for Hamiltonian systems ⋮ Multiple periodic solutions of superlinear ordinary differential equations with a parameter ⋮ Applications of Morse theory to some nonlinear elliptic equations with resonance at zero ⋮ Nontrivial periodic solutions to delay difference equations via Morse theory ⋮ Bounded resonant problems driven by fractional Laplacian ⋮ Gradient systems with sublinear term near the origin and asymptotically linear term near infinity ⋮ Computations of critical groups and periodic solutions for asymptotically linear Hamiltonian systems ⋮ Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems ⋮ Multiple solutions for second-order Hamiltonian systems via computation of the critical groups ⋮ Solutions to a gradient system with resonance at both zero and infinity ⋮ Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations ⋮ Critical point theorem for asymptotically quadratic functional without compactness ⋮ Resonant problems for fractional Laplacian ⋮ Multiple periodic solutions of ordinary differential equations with double resonance ⋮ Multiple solutions for semilinear elliptic boundary value problems with double resonance ⋮ Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero ⋮ Existence and multiplicity of rotating periodic solutions for resonant Hamiltonian systems

Cites Work

• Nontrivial critical points for asymptotically quadratic functions
• Solutions of asymptotically linear operator equations via morse theory
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
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