On sign-changing solutions for resonant (p,q)-Laplace equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43951719" target="_blank" >RIV/49777513:23520/18:43951719 - isvavai.cz</a>
Result on the web
<a href="http://dea.ele-math.com/10-12/On-sign-changing-solutions-for-resonant-(p,q)-Laplace-equations" target="_blank" >http://dea.ele-math.com/10-12/On-sign-changing-solutions-for-resonant-(p,q)-Laplace-equations</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7153/dea-2018-10-12" target="_blank" >10.7153/dea-2018-10-12</a>

Result language
angličtina
Original language name
On sign-changing solutions for resonant (p,q)-Laplace equations
Original language description
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 $alphainsigma(-Delta_p)$ 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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