Titlebook: Index theory in nonlinear analysis; Chungen Liu Book 2019 Springer Nature Singapore Pte Ltd. 2019 Maslov type index.Morse index.P-index.L-

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Applications of ,-Index, global sense started from 1980 in [.]. Since then many mathematicians made their contributions on this problem (cf. [., ., ., ., ., .] and so on). In this section, we consider the non-periodic (.-boundary) solutions of asymptotically linear Hamiltonian systems.

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Applications of ,-Index,theory. In Sect. 9.2, by using the iteration theory of the .-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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Book 2019and P-index theory (index theory for P-boundary conditions). In addition, the book introduces readers to recent advances in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations..

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in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations..978-981-13-7289-6978-981-13-7287-2

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Chungen LiuEquip readers with both L-index theory and P-index theory.Demonstrate recent progress on index theories for a symmetric periodic solution of nonlinear Hamiltonian systems

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A Brief Introduction to Index Functions,For ., we recall that the symplectic group is defined as . where ., .. is the identity matrix on ., and . is the space of 2.?×?2. real matrices. Without confusion, we shall omit the subindex of the identity matrices. For .?>?0, suppose ., where ..

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The ,-Index Theory,If the Hamiltonian function . satisfying .(.?+?., .)?=?.(., .) with .?∈Sp(2.), it is natural to consider the following nonlinear Hamiltonian system with .-boundary condition.