A note on the oscillation problems for differential equations with $p(t)$-Laplacian

Abstract

This paper deals with the oscillation problems on the nonlinear differential equation $(a(t)|x^{\prime }|^{p(t)-2}x^{\prime })^{\prime }+b(t)|x|^{\lambda -2}x=0$ involving $p(t)$-Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.