A necessary and sufficient condition for the existence of positive solutions to singular boundary-value problems of higher order differential equations

Abstract

By constructing some special cones and using fixed point theorem of cone expansion and compression, this paper presents some necessary and sufficient conditions for the existence of $C^{4n-2}$ positive solutions to a class of singular boundary-value problems. Some examples are presented to illustrate our main results.

Keywords

• Singular sublinear boundary-value problem
• positive solution
• fixed point theorem
• cone
• higher order differential equation.