Variational approach to second-order impulsive dynamic equations on time scales

The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will be interested in the solutions of the impulsive nonlinear problem with linear derivative dependence satisfying an impulsive condition.Comment: 17 page

Characterization of the Solvability of Generalized Constrained Variational Equations

In a general context, that of the locally convex spaces, we characterize the existence of a solution for certain variational equations with constraints. For the normed case and in the presence of some kind of compactness of the closed unit ball, more specifically, when we deal with reflexive spaces or, in a more general way, with dual spaces, we deduce results implying the existence of a unique weak solution for a wide class of linear elliptic boundary value problems that do not admit a classical treatment. Finally, we apply our statements to the study of linear impulsive differential equations, extending previously stated results.This research is partially supported by the Junta de Andaluca Grant FQM359

Superlinear damped vibration problems on time scales with nonlocal boundary conditions

This paper studies a class of superlinear damped vibration equations with nonlocal boundary conditions on time scales by using the calculus of variations. We consider the Cerami condition, while the nonlinear term does not satisfy Ambrosetti–Rabinowitz condition such that the critical point theory could be applied. Then we establish the variational structure in an appropriate Sobolev’s space, obtain the existence of infinitely many large energy solutions. Finally, two examples are given to prove our results

On the variational principle and applications for a class of damped vibration systems with a small forcing term

This paper is dedicated to studying the existence of periodic solutions to a new class of forced damped vibration systems by the variational method. The advantage of this kind of system is that the coefficient of its second order term is a symmetric $N \times N$ matrix valued function rather than the identity matrix previously studied. The variational principle of this problem is obtained by using two methods: the direct method of the calculus of variations and the semi-inverse method. New existence conditions of periodic solutions are created through several auxiliary functions so that two existence theorems of periodic solutions of the forced damped vibration systems are obtained by using the least action principle and the saddle point theorem in the critical point theory. Our results improve and extend many previously known results

On well posed impulsive boundary value problems for p(t)-Laplacian's

In this paper we investigate via variational methods and critical point theory the existence of solutions, uniqueness and continuous dependence on parameters to impulsive problems with a p(t)-Laplacian and Dirichlet boundary value conditions