Sign-changing solutions for $p$-Laplacian equations with jumping nonlinearity and the Fučik spectrum
Keywords
Jumping, sign-changing solution, Fučik spectrumAbstract
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.Published
2016-05-29
How to Cite
1.
XIONG, Ming, YANG, Ze-Heng and LIU, Xiang-Qing. Sign-changing solutions for $p$-Laplacian equations with jumping nonlinearity and the Fučik spectrum. Topological Methods in Nonlinear Analysis. Online. 29 May 2016. Vol. 48, no. 1, pp. 159 - 181. [Accessed 29 March 2024].
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