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

Kōdai Fujimoto

Address: Faculty of Liberal Arts, Sciences and Global Education, Osaka Metropolitan University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan

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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.

AMSclassification: primary 34C10; secondary 34C15.

Keywords: oscillation, p(t)-Laplacian, half-linear differential equations.

DOI: 10.5817/AM2023-1-39