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

Kōdai Fujimoto — 2023

Archivum Mathematicum

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

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