Multiple solutions of boundary value problems on time scales for a φ-Laplacian operator

Abstract

We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a $\varphi$-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete $p$-Laplacian as well as those for boundary value problems on time scales.