Nodal Solutions of the p-Laplacian with Sign-Changing Weight

Abstract

We are concerned with determining values of $\gamma$, for which there exist nodal solutions of the boundary value problem ${({|u^{\prime }|}^{p-\mathrm{2}}{u}^{\prime })}^{\prime }+\gamma m(t)f(u)=\mathrm{0},t\in (\mathrm{0,1})$, $u(\mathrm{0})=u(\mathrm{1})=\mathrm{0},$ where $m\in C[\mathrm{0,1}]$ is a sign-changing function, $f:ℝ\to ℝ$ with $f(s)s>\mathrm{0}$. The proof of our main results is based upon global bifurcation techniques.