Yuki Naito, Department of Mathematics, Ehime University, Matsuyama, 790-8577 Japan, e-mail: ynaito@ehime-u.ac.jp
Abstract: We consider the boundary value problem involving the one dimensional $p$-Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.
Keywords: boundary value problem, half-linear differential equation, Sturm comparison theorem, half-linear Prufer transformation
Classification (MSC 2010): 34B15, 34C10
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