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.

Keywords

• dynamic equations on time scales
• nonlinear boundary value problems
• upper and lower solutions
• leray-schauder degree
• multiple solutions