Abstract
In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space \(W^1L^\Phi([0,T])\). We employ the direct method of calculus of variations and we consider a potential function \(F\) satisfying the inequality \(|\nabla F(t,x)|\leq b_1(t) \Phi_0'(|x|)+b_2(t)\), with \(b_1, b_2\in L^1\) and certain \(N\)-functions \(\Phi_0\).
Highlights
It is assumed that the function a : [0, +∞) → [0, +∞) is continuous and non-decreasing, and 0 ≤ b ∈ L1([0, T ], R)
This paper deals with a system of equations of the type: (1)
We are interested in finding periodic weak solutions of
Summary
It is assumed that the function a : [0, +∞) → [0, +∞) is continuous and non-decreasing, and 0 ≤ b ∈ L1([0, T ], R). We say that a non-decreasing function η : R+ → R+ satisfies the ∆∞ 2 -condition, denoted by η ∈ ∆∞ 2 , if there exist constants K > 0 and x0 ≥ 0 such that η(2x) ≤ Kη(x), for every x ≥ x0. If there exists x0 > 0 such that inequality (5) holds for x ≤ x0, we will say that Φ satisfies the ∆02-condition (Φ ∈ ∆02).
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