Applications of L-Index

Chungen Liu
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Chungen Liu: Guangzhou University, School of Mathematical and Information Science

Chapter Chapter 9 in Index theory in nonlinear analysis, 2019, pp 253-273 from Springer

Abstract: Abstract In this chapter, we apply the L-index theory developed in Chap. 5 to study the existence and multiplicity of L-solutions of nonlinear Hamiltonian systems. In Sect. 9.1, we consider the existence of brake solution of asymptotically linear Hamiltonian system via the variational method and the L-index theory. In Sect. 9.2, by using the iteration theory of the L-index, we consider the minimal periodic problem for brake solutions of super-quadratic autonomous Hamiltonian systems. In Sect. 9.3, we obtain an infinitely many brake solutions of super-quadratic non-autonomous Hamiltonian systems.

Date: 2019
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DOI: 10.1007/978-981-13-7287-2_9

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