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

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Abstract

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.

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  1. Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu, 210097, People’s Republic of China

    Yujun Dong

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  1. Yujun Dong
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Dong, Y. Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations. Calc. Var. 38, 75–109 (2010). https://doi.org/10.1007/s00526-009-0279-5

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  • DOI: https://doi.org/10.1007/s00526-009-0279-5

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