Extremal solutions for p-laplacian differential systems via iterative computation

Abstract

In this paper, we study the extremal solutions of a fractional differential system involving the pp-Laplacian operator and nonlocal boundary conditions. The conditions for the existence of the maximal and minimal solutions to the system are established. In addition, we also derive explicit formulae for the estimation of the lower and upper bounds of the extremal solutions, and establish a convergent iterative scheme for finding these solutions. We also give a special case in which the conditions for the existence of the extremal solutions can be easily verified.