Existence of positive solutions of a terminal value problem for fourth-order differential equations

Abstract

We are concerned with the existence of positive solutions of a terminal value problem for a class of fourth-order differential equation. Our arguments are based to establish sufficient conditions which guarantee the existence of at least one positive solution by constructing a cone on which a positive operator is defined. We then apply a theorem of Guo-Krasonelskii to prove the existence of positive solutions of our problem.

Keywords

• fourth order differential equation
• positive solutions
• guo-krasnoselskii theorem
• cone preserving map