Leighton–Wintner type oscillation criteria for second-order differential equations with $p(t)$-Laplacian - Kōdai Fujimoto; Masakazu Onitsuka (Electronic Journal of Qualitative Theory of Differential Equations)
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.