P-Laplacian Dirac system on time scales

Abstract

The $ {p} $ -Laplacian type Dirac systems are nonlinear generalizations of the classical Dirac systems. They can be observed as a bridge between nonlinear systems and linear systems. The purpose of this study is to consider $ {p} $ -Laplacian Dirac boundary value problem on an arbitrary time scale to get forceful results by examining some spectral properties of this problem on time scales. Interesting enough, the $ {p} $ -Laplacian type Dirac boundary value problem exhibits the classical Dirac problem on time scales. Moreover, we prove Picone's identity for $ {p} $ -Laplacian type Dirac system which is an important tool to prove oscillation criteria on time scales. It generalizes a classical and well-known theorem for $ {p=2} $ to general case $ {p>1.} $

Keywords

• dirac system
• laplacian operator
• time scales