Existence of solutions for subquadratic convex or $B$-concave operator equations and applications to second order Hamiltonian systems

This paper investigates solutions for subquadratic convex or $B$-concave operator equations. First, some existence results are obtained by the index theory and the critical point theory. Then, some applications to second order Hamiltonian systems satisfying generalized periodic boundary value condit...

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Published in:Electronic journal of qualitative theory of differential equations 2020-01, Vol.2020 (49), p.1-19
Main Author: Song, Mingliang
Format: Article
Language:English
Subjects:
critical point
index theory
operator equations
second order hamiltonian systems
subquadratic
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description This paper investigates solutions for subquadratic convex or $B$-concave operator equations. First, some existence results are obtained by the index theory and the critical point theory. Then, some applications to second order Hamiltonian systems satisfying generalized periodic boundary value conditions and Sturm–Liouville boundary value conditions are pointed out. In particular, some well known theorems about periodic solutions for second order Hamiltonian systems are special cases of these results.
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subjects critical point
index theory
operator equations
second order hamiltonian systems
subquadratic
title Existence of solutions for subquadratic convex or $B$-concave operator equations and applications to second order Hamiltonian systems
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