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

Details Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations Index theory for linear self-adjoint operator equations and nontrivial solutions for asymptotically linear operator equations

2007-05-13

arxiv.org/abs/0705.1811v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We will first establish an index theory for linear self-adjoint operator equations. And then with the help of this index theory we will discuss existence and multiplicity of solutions for asymptotically linear operator equations by making use of the dual variational methods and Morse theory. Finally, some interesting examples concerning second order Hamiltonian systems, first order Hamiltonian systems and elliptical partial differential equations will be presented to illustrate our results.

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