Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations

By Yujun Dong. 2007

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We develop index theories for linear selfadjoint operator equations and investigate multiple solutions for asymptotically linear operator equations. The operator equations consist of two kinds: the first has finite Morse index and can be used to investigate second order Hamiltonian systems and elliptic partial differential equations; the second may have infinite Morse index and can be used to investigate first order Hamiltonian systems.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a72c3b95588a9dbeb5d8ae87a4d2534171dfe43