Picone’s identity for -Laplace operator and its applications

UDC 517.9We prove a nonlinear analogue of Picone's identity for -Laplace operator. As an application, we give a Hardy type inequality and Sturmian comparison principle.We also show the strict monotonicity of the principle eigenvalue and degenerate elliptic system.

Some Spectral Properties of p-Laplacian Diffusion Boundary Value Problem on Time Scales

In this paper, we consider p-Laplacian type Diffusion boundary value problem on an arbitrary time scale. We generalize some spectral properties of p-Laplacian Diffusion problem to an arbitrary time scale. Moreover, we prove Picone's identity for this problem.