Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations. (20th August 2015)

• Record Type: Journal Article
• Authors: Yan, Baoqiang; Zhang, Meng
• Other Names: Infante Gennaro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-08-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/620251
• Languages: English
• ISSNs: 2314-8896

Abstract

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.