Exact Number of Positive Solutions for a Class of Two-Point Boundary Value Problems

Abstract

This paper considers the existence of positive solutions of the boundary value problems $v^{\prime \prime }+\lambda (v^r+v^p-v^q)=0$ and $v(-1)=v(1)=0$, where $p>r>q>-1$ and $\lambda$ is a positive parameter. Using a time-map approach, we obtain the exact number of positive solutions in different cases.