On the Solvability of Fourth-Order Two-Point Boundary Value Problems

Abstract

In this paper, we study the solvability of various two-point boundary value problems for x ( 4 ) = f ( t , x , x ′ , x ″ , x ‴ ) , t ∈ ( 0 , 1 ) , where f may be defined and continuous on a suitable bounded subset of its domain. Imposing barrier strips type conditions, we give results guaranteeing not only positive solutions, but also monotonic ones and such with suitable curvature.

Keywords

• fourth-order differential equation
• two-point boundary value problems
• existence
• positive or non-negative, monotone, convex or concave solutions
• sign conditions