Periodic Solutions for Second Order Systems with Not Uniformly Coercive Potential

Abstract

The existence and multiplicity of periodic solutions are obtained for the nonau-Ž . tonomous second order systems with locally coercive potential; that is, F t, x ª < < w x qϱ as x ª ϱ for a.e. t in some positive-measure subset of 0, T , by using an analogy of Egorov's Theorem, the properties of subadditive functions, the least action principle, and a three-critical-point theorem proposed by Brezis and Nirenberg. ᮊ

Non-autonomous second order Hamiltonian systems

“…Similar conditions on the potential with some generalizations appear in the work of Tang [118,119,121,122], Tang and Wu [124,125,127] [41] gave conditions for solutions in the case when as |x| → ∞ the sign of the potential is negative and the magnitude is bounded above and below by a multiple of |x| 2 .…”

Nonautonomous second order Hamiltonian systems

“…t ∈ I . Subsequently, Willem [1981], Mawhin [1987], Mawhin and Willem [1989], Tang [1995;1998], Tang and Wu [1999;2001; and others (see the references therein) proved existence under various conditions. The periodic problem (1-1) was studied by Mawhin and Willem [1986;1989], Long [1995], Tang and Wu [2003] and others.…”

A Multiplicity Theorem for a Perturbed Second-Order Non-Autonomous System

“…In this paper we consider the second-order non-autonomous system ü = α(t) ( It is well known (see [3]) that a solution of (P λ ) is a function u ∈ C 1 ([0, T ], R N ), witḣ u absolutely continuous, such that the existence of at least three solutions has previously been studied in [1], [6], [7] and [9] under the following assumption, firstly introduced by Brezis and Nirenberg: there exist r > 0 and an integer k 0 such that…”