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

This paper deals with the oscillation problems on the nonlinear differential equation $\left(a\left(t\right)\right|{x}^{\text{'}}{|}^{p\left(t\right)-2}{x}^{\text{'}}{)}^{\text{'}}+b\left(t\right){\left|x\right|}^{\lambda -2}x=0$ involving $p\left(t\right)$-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.