$\phi $-Laplacian BVPs with linear bounded operator conditions

Kamal Bachouche, Smaïl Djebali, and Toufik Moussaoui

National Higher School of Statistics and Applied Economics, 11, Doudou Moukhtar St. Ben-Aknoun, Algiers, Algeria
Department of Mathematics, École Normale Supérieure, PB 92, 16050 Kouba, Algiers, Algeria


Abstract: The aim of this paper is to present new existence results for $\phi $-Laplacian boundary value problems with linear bounded operator conditions. Existence theorems are obtained using the Schauder and the Krasnosel’skii fixed point theorems. Some examples illustrate the results obtained and applications to multi-point boundary value problems are provided.

AMSclassification: primary 34B10; secondary 34B15, 34B18.

Keywords: \phi -Laplacian, BVPs, Krasnosel’skii’s fixed point theorem, Schauder’s fixed point theorem.

DOI: 10.5817/AM2012-2-121