Nontrivial solutions for a fourth-order Riemann-Stieltjes integral boundary value problem

Abstract

In this paper we study a fourth-order differential equation with Riemann-Stieltjes integral boundary conditions. We consider two cases, namely when the nonlinearity satisfies superlinear growth conditions (we use topological degree to obtain an existence theorem on nontrivial solutions), when the nonlinearity satisfies a one-sided Lipschitz condition (we use the method of upper-lower solutions to obtain extremal solutions).

Keywords

• fourth-order differential equation
• integral boundary value problem
• topological degree
• upper-lower solution
• nontrivial solutions
• extremal solutions