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 article |
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) OBD |
Files in This Item:
File | Size | Format | |
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BobkovTanaka_Nodal_solutions2_2018.pdf | 180,46 kB | Adobe PDF | View/Open |
Please use this identifier to cite or link to this item:
http://hdl.handle.net/11025/30449
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