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Keywords:
oscillation; $p(t)$-Laplacian; half-linear differential equations
oscillation; $p(t)$-Laplacian; half-linear differential equations
Summary:
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.
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