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

Ming Xiong, Ze-Heng Yang, Xiang-Qing Liu

DOI: http://dx.doi.org/10.12775/TMNA.2016.041

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.

Keywords


Jumping; sign-changing solution; Fučik spectrum

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