Skip to main content
Article thumbnail
Location of Repository

Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations(II)

By Yujun Dong and Yuan Shan

Abstract

Reference [1] established an index theory for a class of linear selfadjoint operator equations covering both second order linear Hamiltonian systems and first order linear Hamiltonian systems as special cases. In this paper based upon this index theory we construct a new reduced functional to investigate multiple solutions for asymptotically linear operator equations by Morse theory. The functional is defined on an infinite dimensional Hilbert space, is twice differentiable and has a finite Morse index. Investigating critical points of this functional by Morse theory gives us a unified way to deal with nontrivial solutions of both asymptotically second order Hamiltonian systems and asymptotically first order Hamiltonian systems

Topics: Mathematics - Classical Analysis and ODEs
Year: 2011
OAI identifier: oai:arXiv.org:1104.1670
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1104.1670 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.