Types and Multiplicity of Solutions to Sturm–liouville Boundary Value Problem

Abstract

Abstract. We consider the second-order nonlinear boundary value problems (BVPs) with Sturm-Liouville boundary conditions. We define types of solutions and show that if there exist solutions of different types then there exist intermediate solutions also.Keywords: nonlinear boundary value problem, multiplicity of solutions, Sturm-Liouville problem.

On Different Type Solutions of Boundary Value Problems

“…Suppose solutions x(t, γ * ) and x(t, γ * ) are of types n and m respectively and |n−m| ≥ 2. Then there exist at least |n−m−1| more solutions of the BVP.This assertion was proved in[2].…”