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.

Keywords

• oscillation
• second-order differential equation
• $p(t)$-laplacian
• quasilinear differential equation
• emden–fowler differential equation
• riccati technique