Existence and multiplicity of solutions of a fourth order equation

Abstract

In this paper we study the existence and multiplicity of solutions of the fourth order nonlinear boundary value problem is assumed to be positive, continuous and increasing in y.

We prove that there exists a λ⁺ >0 such that there is always a solution for . From our results it follows that if is bounded (for x in some compact interval around 1/2) then there exists λ ₊ such that there is no solution for λ>λ ₊. Under certain conditions on f we find λ _∗, such that there are at least two solutions for 0>λ>λ _∗. Fdzed point index is used to prove this result.

Keywords:

• Fourth order equation
• Nonlinear differential equation
• Leray-Schauder degree
• Nonlinear