Title: On sign-changing solutions for resonant (p,q)-Laplace equations
Authors: Bobkov, Vladimír
Tanaka, Mieko
Issue Date: 2018
Publisher: Ele-Math
Document type: článek
URI: http://hdl.handle.net/11025/30449
ISSN: 1847-120X
Keywords in different language: (p,q) -Laplacian;generalized eigenvalue problem;nodal solutions;linking methods;indefinite nonlinearity.
Abstract in different language: We provide two existence results for sign-changing solutions to the Dirichlet problem for the family of equations $-\Delta_p u -\Delta_q u = \alpha |u|^{p-2}u + \beta |u|^{q-2}u$, where $1<q<p$ and $\alpha$, $\beta$ are parameters. First, we show the existence in the resonant case $\alpha\in\sigma(-\Delta_p)$ for sufficiently large $\beta$, thereby generalizing previously known results. The obtained solutions have negative energy. Second, we show the existence for any $\beta \geq \lambda_1(q)$ and sufficiently large $\alpha$ under an additional nonresonant assumption, where $\lambda_1(q)$ is the first eigenvalue of the $q$-Laplacian. The obtained solutions have positive energy.
Rights: © Ele-Math
Appears in Collections:Články / Articles (KMA)

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