Abstract
In this paper, some existence theorems are obtained for subharmonic solutions of second-order Hamiltonian systems with linear part under non-quadratic conditions. The approach is the minimax principle. We consider some new cases and obtain some new existence results.MSC:34C25, 58E50, 70H05.
Highlights
Where A is an N × N symmetric matrix and F : R × RN → R is T-periodic in t and satisfies the following assumption: Assumption (A) F(t, x) is measurable in t for every x ∈ RN and continuously differentiable in x for a.e. t ∈ [, T], and there exist a ∈ C(R+, R+) and b : R+ → R+ which is T -periodic and b ∈ Lp(, T; R+) with p > such that
In our Theorem . and Theorem . , we study the existence of subharmonic solutions for system ( . ) from a different perspective. λi (i ∈ {, . . . , r}) in our theorems are the eigenvalues of the matrix A
We present a result about the existence of subharmonic solutions for system ( . )
Summary
Where A is an N × N symmetric matrix and F : R × RN → R is T-periodic in t and satisfies the following assumption: Assumption (A) F(t, x) is measurable in t for every x ∈ RN and continuously differentiable in x for a.e. t ∈ [ , T], and there exist a ∈ C(R+, R+) and b : R+ → R+ which is T -periodic and b ∈ Lp( , T; R+) with p > such that ) under the following AR-condition: there exist μ > and L > such that They considered the existence of subharmonic solutions and obtained the following result.
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