Computations of critical groups and applications to some differential equations at resonance

DOI10.1016/j.na.2006.07.044zbMath1123.58007OpenAlexW2122834612MaRDI QIDQ2371175

Zhi-Qing Han

Publication date: 29 June 2007

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.2006.07.044

zbMATH Keywords

critical groupsMorse theorynontrivial solutionselliptic boundary value problemsecond order Hamiltonian system

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear boundary value problems for ordinary differential equations (34B15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05)

Related Items (7)

Existence of solutions for a class of operator equations ⋮ Periodic solutions for asymptotically linear Hamiltonian system with resonance both at infinity and origin via computation of critical groups ⋮ Solutions of periodic boundary value problems for second-order nonlinear differential equations via variational methods ⋮ Existence of solutions for 2\(m\)th-order periodic boundary value problems ⋮ Nonautonomous nonlinear ODEs: nonresonance conditions and rotation numbers ⋮ Existence of multiple solutions of a second-order difference boundary value problem ⋮ Periodic solutions to second order nonautonomous differential systems with unbounded nonlinearities

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