Results of existence of non-trivial weak solutions for a boundary value problem

Abstract

The objective of this thesis is to study and demonstrate the existence of at least three weak solutions for a certain class of boundary value problems for nonlinear fractional differential systems. The first part is devoted to the notions of functional analysis and also to the definitions used in this work, also it presents the fundamental theorems implemented to demonstrate the existence of the solutions. Then, the necessary background to familiarize the reader with fractional calculus and the main issues related to the research is provided. We demonstrate the existence of three weak solutions by the variational method and theorem of Bonanno and Marano for new class of fractional p-Laplacian boundary value systems. In the second part we prove the existence of the multiple solutions for perturbed nonlinear fractional p-Laplacian boundary value systems with two control parameters by using of the critical point theorem of Ricceri