## Topological Methods in Nonlinear Analysis

### Sign-changing solutions for $p$-Laplacian equations with jumping nonlinearity and the Fučik spectrum

#### Abstract

We study the existence of sign-changing solutions for the $p$-Laplacian equation $$-\Delta_pu +\lambda g(x)|u|^{p-2}u=f(u),\quad x\in \mathbb{R}^N,$$ where $\lambda$ is a positive parameter and the nonlinear term $f$ has jumping nonlinearity at infinity and is superlinear at zero. The Fučik spectrum plays an important role in the proof. We give sufficient conditions for the existence of nontrivial Fučik spectrum.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 1 (2016), 159-181.

Dates
First available in Project Euclid: 30 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475266376

Digital Object Identifier
doi:10.12775/TMNA.2016.041

Mathematical Reviews number (MathSciNet)
MR3561427

Zentralblatt MATH identifier
1368.35152

#### Citation

Xiong, Ming; Yang, Ze-Heng; Liu, Xiang-Qing. Sign-changing solutions for $p$-Laplacian equations with jumping nonlinearity and the Fučik spectrum. Topol. Methods Nonlinear Anal. 48 (2016), no. 1, 159--181. doi:10.12775/TMNA.2016.041. https://projecteuclid.org/euclid.tmna/1475266376

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