Multiple solutions of nonlinear boundary value problems with oscillatory solutions

Abstract

We consider two second order autonomous differential equations with critical points, which allow the detection of an exact number of solutions to the Dirichlet boundary value problem. Non‐autonomous equations with similar behaviour of solutions also are considered. Estimations from below of the number of solutions to the Dirichlet boundary value problem are given. First Published Online: 14 Oct 2010

Keywords

• singular points
• multiple solutions
• heteroclinic solutions
• homoclinic solutions