Some notes on a superlinear second order Hamiltonian system

Abstract

Variational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered.

Existence of Periodic Solutions for Second-Order Ordinary p-Laplacian Systems

“…The existence and multiplicity of periodic solutions to problem (2) were obtained on various hypotheses on the potential function F(t, x) or nonlinearity ∇F(t, x) (see, Refs. [1][2][3][4][5][6]).…”

Existence of Solutions for Superlinear Second-Order System with Noninstantaneous Impulses

“…However, in [11,12], the authors considered a kind of noninstantaneous impulsive effects, which is motivated by paper [13]. On the other hand, in recent years, some new critical point theorems are used to study nonlinear differential equations with no impulsive effects (see for example, [14][15][16][17][18][19][20][21]). Based on these two facts, we investigate the existence of nontrivial solution for (1).…”

Two positive solutions for a Dirichlet problem with the (p,q)‐Laplacian

“…About other results of existence of at least two solutions for different type of differential problems we refer for instance to [6–8, 12, 13, 15, 29] and references therein.…”