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.
