RELATION OF POSITIVE SOLUTIONS FOR SUPERLINEAR M-LAPLACIAN BVPS AND ITS APPLICATIONS

Abstract

In this article, we will classify the relations of two distinct
positive solutions for the superlinear m-Laplacian boundary value
problems
\[
\quad\qquad (BVP)~~~~~~~ \left\{
\begin{array}{ll}
&\displaystyle {(E)~~(\psi (r)|u'|^{m-2} u')'+\psi
(r)f(r,u)=0~~~~~\hbox{~~in~~}~~~~~(0,1)}\\
&\displaystyle {(BC)~~u'(0)=u(1)=0.}\\
\end{array}\right.
\]
Furthermore, we will use these relations of positive solutions to
establish some criterion for the uniqueness of positive solutions
of (BVP).