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Open Access Research

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

Victoria Otero-Espinar1* and Tania Pernas-Castaño12

Author Affiliations

1 Departamento de Análise Matemática, Universidade de Santiago de Compostela, Santiago de Compostela, Galicia, 15782, Spain

2 Instituto de Ciencias Matemáticas (CSIC, UAM, UC3M, UCM), Madrid, 28049, Spain

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Boundary Value Problems 2013, 2013:119  doi:10.1186/1687-2770-2013-119

Published: 9 May 2013

Abstract

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

MSC: 34B37, 34N05.

Keywords:
impulsive dynamic equations; second-order boundary value problem; variational techniques; critical point theory; time scales