Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Jean Mawhin,Ewa Skrzypek,Katarzyna Szymań ska-Dȩ bowska

Affiliation:	1.Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium;2.Institute of Mathematics, Lodz University of Technology, Al. Politechniki 10, 93-590 Łódź, Poland;

Abstract:	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.

Keywords:	du Bois– Reymond lemma, p(t)– Laplacian, time scales, variational methods, direct variational method, mountain pass lemma