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2017 Sign-changing solutions to a class of nonlinear equations involving the $p$-Laplacian
Wei-Chuan Wang, Yan-Hsiou Cheng
Rocky Mountain J. Math. 47(3): 971-996 (2017). DOI: 10.1216/RMJ-2017-47-3-971

Abstract

This paper deals with a class of nonlinear problems $$ -(r^{n-1}|u'|^{p-2}u')'+r^{n-1}q(r)|u|^{p-2}u =r^{n-1}w(r)f(u) $$ in $(0,1)$, where $1\leq n\lt p\lt \infty $ and $'={d}/{dr}$. We study the existence of nodal solutions to this nonautonomous system. We give necessary and sufficient conditions for the existence of sign-changing solutions and also observe an application related to the case of multi-point boundary conditions. Methods used here are energy function control, shooting arguments and Pr\"{u}fer-type substitutions.

Citation

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Wei-Chuan Wang. Yan-Hsiou Cheng. "Sign-changing solutions to a class of nonlinear equations involving the $p$-Laplacian." Rocky Mountain J. Math. 47 (3) 971 - 996, 2017. https://doi.org/10.1216/RMJ-2017-47-3-971

Information

Published: 2017
First available in Project Euclid: 24 June 2017

zbMATH: 1371.34039
MathSciNet: MR3682158
Digital Object Identifier: 10.1216/RMJ-2017-47-3-971

Subjects:
Primary: 34A12, 34B15

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 3 • 2017
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