Positive solutions of a three-point boundary-value problem for differential equations with damping and actively bounded delayed forcing term

Abstract

We provide sufficient conditions for the existence of positive solutions of a three-point boundary value problem concerning a second order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning introduced in [19]. By writing the damping term as a difference of two factors one can extract more information on the solutions. (For instance, in an application, given in the last section, we can give the exact value of the norm of the solution).

Keywords

• Boundary value problems
• delay differential equations
• positive solutions
• actively bounded functions
• Krasnoselskii fixed point theorem.