Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations. (20th August 2015) - Yan, Baoqiang; Zhang, Meng
Abstract : This paper considers the following boundary value problem:( ( - u ' ( t ) ) n ) ' = n t n - 1 f ( u ( t ) ),     0 < t < 1,     u ' ( 0 ) = 0,     u ( 1 ) = 0, wheren > 1 is 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.