Du Bois-Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)-Laplacian on a Bounded Time Scale.

This paper is devoted to study the existence of solutions and their regularity in the p(t)-Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois-Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem.