Some abstract critical point theorems for self-adjoint operator equations and applications

Abstract

By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent, the authors discuss the existence and multiplicity of solutions for (nonlinear) operator equations, and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.

Keywords

Self-adjoint operator equations / Index theory / Relative Morse index / Dual variational method / Morse theory / Hamiltonian systems

References

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