Existence of solutions for fourth-order nonlinear boundary value problems

Abstract

Abstract In this paper, we discuss the existence and approximation of solutions for a fourth-order nonlinear boundary value problem by using a quasilinearization technique. In the presence of a lower solution α and an upper solution β in the reverse order α ≥ β $\alpha \geq \beta $ , we show the existence of (extreme) solution.

Keywords

• Boundary value problem
• Quasilinearization method
• Upper solution and lower solution
• Extreme solution