Existence for Two-Point <i>n</i>th Order Boundary Value Problems under Barrier Strips

Abstract

Using barrier strip conditions, we study the solvability of two-point boundary value problems for the equation x(n)=f(t,x,x′,…,x(n−1)). In the case n=4, we apply the used approach to obtain results guaranteeing positive or non-negative, monotone, convex solutions to boundary value problems with various boundary conditions.

Keywords

• <i>n</i>th and fourth-order differential equations
• two-point boundary conditions
• existence
• barrier strips