Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations

Abstract

This paper considers the following boundary value problem:((-u'(t))n)'=ntn-1f(u(t)),  0<t<1,  u'(0)=0,  u(1)=0, wheren>1is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions.