2009
DOI: 10.1007/s00526-009-0279-5
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Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations

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. Mathematics Subject Classification (2000)

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Cited by 42 publications
(53 citation statements)
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“…[6,Theorem 3.1.7], the functional Φ behaves as a quadratic functional at infinity but in our Theorem 1.2 it is only required that the functional Φ is estimated from below by a quadratic functional.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…[6,Theorem 3.1.7], the functional Φ behaves as a quadratic functional at infinity but in our Theorem 1.2 it is only required that the functional Φ is estimated from below by a quadratic functional.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…In [13], the authors established the existence and multiplicity of solutions to the abstract self-adjoint operator equation via Morse theory. In this paper, instead of Morse theory, we make use of minimax arguments for multiplicity of critical points in the presence of symmetry.…”
Section: Remark 12 Frommentioning
confidence: 99%
“…In [12], Dong established an index theory by the concept of relative Morse index and dual variational methods. The authors constructed that in [13] for the infinitely unbounded case.…”
Section: Remark 12 Frommentioning
confidence: 99%
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