Three periodic solutions for perturbed second order Hamiltonian systems

Abstract

In this paper we study the existence of three distinct solutions for the following problemwhere λ ∈ R, T is a real positive number, A : [0, T ] → R N×N is a continuous map from the interval [0, T ] to the set of N-order symmetric matrices. We propose sufficient conditions only on the potential F . More precisely, we assume that G satisfies only a usual growth condition which allows us to use a variational approach.

Homoclinic solutions for a class of subquadratic second-order Hamiltonian systems

“…Inspired by the excellent monographs [1,2], by now, the existence and multiplicity of periodic and homoclinic solutions for second-order Hamiltonian systems have been extensively investigated in many papers (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein) via variational methods. Also second-order Hamiltonian systems with impulses via variational methods have been recently considered in [20][21][22].…”

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 .…”

Solvability of a class of impulsive damped vibration problems

“…When p 2 L 2 .0, T; R C /, in a way similar to the proof of (40), it follows from (16), (33), and (39) that…”

“…The existence of solution for problem (9) has been studied extensively (see e.g., [11,12,14,[29][30][31][32][33][34][35][36]), in particular, when the gradient…”