The existence of weak positive solutions of the elliptic problem via the Sub-supersolution method

Abstract

The object of this thesis is to study the existence of weak positive solutions to Kirchho¤ s elliptic problems by using the Sub-supersolution method. The problem that studied is called nonlocal due to the presence of the Kirchho¤ operator M( R

1 p(x)jrujp(x)dx);where M is a continuous and increasing function on R+ and its values are completely positive.This means that the equation is no longer point-identical.This causes some mathematical di¢ culties that make studying such a problem interesting. It is for this reason that we have performed con ning the solution with two weak positive solutions using the Sub-supersolution method.