On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems

Abstract

Under barrier strips type assumptions we study the existence of C 3 [ 0 , 1 ] —solutions to various two-point boundary value problems for the equation x ‴ = f ( t , x , x ′ , x ″ ) . We give also some results guaranteeing positive or non-negative, monotone, convex or concave solutions.

Keywords

• third-order differential equation
• boundary value problem
• existence
• sign conditions