Periodic solutions for second-order Hamiltonian systems with a p-Laplacian

Abstract

Abstract. In this paper, by using the least action principle, Sobolev's inequality and Wirtinger's inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature. Introduction.Consider the second-order Hamiltonian systems (|x|)b(t), |∇F (t, x)| ≤ a(|x|)b(t)for all x ∈ R N and a.e. t ∈ [0, T ].

Some existence results on periodic solutions of Euler–Lagrange equations in an Orlicz–Sobolev space setting

“…As we shall see in Theorem 5.3, when L satisfies (2)-(4), (32) and (33), the coercivity of the action integral I is related to the coercivity of the functional…”

“…Let L be a Lagrangian function satisfying (2)-(4), (32) and (33). Let L be a Lagrangian function satisfying (2)-(4), (32) and (33).…”

“…By using the dual least action principle, in [33] it was performed the extension of some results given in [23]; and, in [32] the authors improved the work done in [34]. By using the dual least action principle, in [33] it was performed the extension of some results given in [23]; and, in [32] the authors improved the work done in [34].…”

Existence of periodic solutions for sublinear second order dynamical system with (q, p)-Laplacian

“…Many solvability conditions are given, such as the coercive condition (see [1]), the periodicity condition (see [8]); the convexity condition (see [2]); the subadditive condition (see [7]). In [9] and [10] By using the least action principle and the generalized saddle point theorem, the authors obtained some existence results. They first improved the classical Poincaré-Wirtinger inequality and then by using some analytical techniques, they improved the condition like the following (1.5).…”

“…In our paper, we will use the improved Poincaré-Wirtinger inequality and some analytical techniques in [9] and [10] to consider system (1.1). Our main results are the following theorems.…”