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.
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Liu, C. (2019). Applications of L-Index. In: Index theory in nonlinear analysis. Springer, Singapore. https://doi.org/10.1007/978-981-13-7287-2_9
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DOI: https://doi.org/10.1007/978-981-13-7287-2_9
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