Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems |
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Authors: | Yujun Dong |
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Affiliation: | Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, PR China |
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Abstract: | In this paper, we consider the existence and multiplicity of solutions of second-order Hamiltonian systems. We propose a generalized asymptotically linear condition on the gradient of Hamiltonian function, classify the linear Hamiltonian systems, prove the monotonicity of the index function, and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear Hamiltonian systems by global analysis methods such as the Leray-Schauder degree theory, the Morse theory, the Ljusternik-Schnirelman theory, etc. |
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Keywords: | Second-order Hamiltonian system Multiple solutions Generalized asymptotically linear conditions Index theory for linear second-order Hamiltonian systems Leray-Schauder degree theory Morse theory Ljusternik-Schnirelman theory |
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