## Rocky Mountain Journal of Mathematics

### Sign-changing solutions to a class of nonlinear equations involving the $p$-Laplacian

#### 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.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 3 (2017), 971-996.

Dates
First available in Project Euclid: 24 June 2017

https://projecteuclid.org/euclid.rmjm/1498269820

Digital Object Identifier
doi:10.1216/RMJ-2017-47-3-971

Mathematical Reviews number (MathSciNet)
MR3682158

Zentralblatt MATH identifier
1371.34039

#### Citation

Wang, Wei-Chuan; Cheng, Yan-Hsiou. Sign-changing solutions to a class of nonlinear equations involving the $p$-Laplacian. Rocky Mountain J. Math. 47 (2017), no. 3, 971--996. doi:10.1216/RMJ-2017-47-3-971. https://projecteuclid.org/euclid.rmjm/1498269820

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