Multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Sturm-Liouville boundary conditions

DOI10.1016/J.NA.2011.04.053zbMath1226.34023OpenAlexW2063086722MaRDI QIDQ550236

Yuan Shan

Publication date: 8 July 2011

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.2011.04.053

zbMATH Keywords

critical pointmultiple solutionsindex theorydual variational principleSturm-Liouville boundary conditions\(\mu\)-indexeven Hamiltonian systemrelative Morse index

Mathematics Subject Classification ID

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 (5)

Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations ⋮ Multiple solutions for generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions ⋮ A twist condition and multiple solutions of unbounded self-adjoint operator equation with symmetries ⋮ Unnamed Item ⋮ Index theory for second order linear Hamiltonian systems with \(L^1\) coefficient matrix satisfying generalized periodic boundary value conditions

Cites Work

• Unnamed Item
• Relative Morse index and multiple brake orbits of asymptotically linear Hamiltonian systems in the presence of symmetries
• Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations
• Branches of index-preserving solutions to systems of second order ODEs
• Infinite dimensional Morse theory and multiple solution problems
• Relative Morse index and its application to Hamiltonian systems in the presence of symmetries
• On equivalent conditions for the solvability of the equation \((p(t)x')'+f(t,x)=h(t)\) satisfying linear boundary conditions with \(f\) restricted by linear growth conditions
• Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems
• Maslov type index theory for linear Hamiltonian systems with Bolza boundary value conditions and multiple solutions for nonlinear Hamiltonian systems
• Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ²
• On Critical Point Theory for Indefinite Functionals in The Presence of Symmetries

This page was built for publication: Multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Sturm-Liouville boundary conditions