Leighton–Wintner type oscillation criteria for second-order differential equations with p ( t ) -Laplacian

Abstract

This paper deals with the oscillation problems for nonlinear differential equations of the form ( r ( t ) | x ′ | p ( t ) − 2 x ′ ) ′ + c ( t ) f ( x ) = 0 involving p ( t ) -Laplacian. The Leighton–Wintner type oscillation criteria are established without any conditions on the limit of p ( t ) . In addition, we discuss the applications to partial differential equations. Some examples are given to illustrate our results.