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Keywords:
boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation
boundary value problem; half-linear differential equation; Sturm comparison theorem; half-linear Prüfer transformation
Summary:
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.
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