On the Dirichlet problem for the $n, alpha$-Laplacian with the nonlinearity in the critical growth range

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10099072" target="_blank" >RIV/00216208:11320/11:10099072 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.na.2011.05.015" target="_blank" >http://dx.doi.org/10.1016/j.na.2011.05.015</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2011.05.015" target="_blank" >10.1016/j.na.2011.05.015</a>

Result language
angličtina
Original language name
On the Dirichlet problem for the $n, alpha$-Laplacian with the nonlinearity in the critical growth range
Original language description
Let $Omegasubseter^n$, $n geq 2$, be a bounded domain. Applying the Mountain Pass Theorem we prove the existence of a~non-trivial weak solution to the Dirichlet problem $$ %uin W_0^1L^{Phi}(Omega)qquadtext{and}qquad -divergence Bigl(Phi''(|nabla u|)frac{nabla u}{|nabla u|}Bigr) =f(x,u)quadtext{ in }Omega , $$ where $u$ is in the Sobolev-Orlicz space $W_0^1L^{Phi}(Omega)$ with a~Young function of the type $Phi(t)approx t^nlog^{alpha}(t)$, $alphan-1$, and $|f(x,t)|approx exp(beta|t|^{frac{n}{n-1-alpha}})$, $beta0$.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F08%2F0383" target="_blank" >GA201/08/0383: Function Spaces, Weighted Inequalities and Interpolation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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