Solvability of a nonlinear second order conjugate eigenvalue problem on a time scale

Abstract

We consider the nonlinear second order conjugate eigenvalue problem on a time scale: $y{}^{\Delta \Delta }\left(t\right)+\lambda a\left(t\right)f\left(y\left(\sigma \left(t\right)\right)\right)=0,t\in \left[0,1\right],y\left(0\right)=0=y\left(\sigma \left(1\right)\right)$ . Values of the parameter $\lambda$ (eigenvalues) are determined for which this problem has a positive solution. The methods used here extend recent results by allowing for a broader class of functions for $a\left(t\right)$.