Maslov type index theory for linear Hamiltonian systems with Bolza boundary value conditions and multiple solutions for nonlinear Hamiltonian systems

Abstract

We study the classification of linear Hamiltonian systems satisfying Bolza boundary conditions and its applications to nonlinear Hamiltonian systems.

Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations

“…The summand denoted by I a (B 1 , B 2 ) is called the relative Morse index between B 1 and B 2 with respect to a(·, ·) as in [12][13][14].…”

“…Unfortunately, the proofs in [13,Theorem 3.8] and [14,Theorem 5.3] are not complete because for example the functional defined in [13, 3.20] is not C 2 , as the referee pointed out. We will give correct proofs in a separate paper.…”

“…Using the new index theory of this paper allows us get some new results. Some special cases have already been discussed by the author in [12][13][14].…”

Asymptotically linear Hamiltonian systems with Lagrangian boundary conditions

“…We follow the ideas of the proof of Lemma II.5.1 in [Chang 1981] to prove (4-9). See [Dong 2005] and [Liu 2005b] for some similar computations.…”

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

“…In sec. 3 we study the relationship between the Maslov-type index defined in [3] and the μ 1 index defined in [1].…”