Ground states of weighted 4D biharmonic equations with exponential growth

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU150389" target="_blank" >RIV/00216305:26220/24:PU150389 - isvavai.cz</a>
Result on the web
<a href="https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001135266200001" target="_blank" >https://www-webofscience-com.ezproxy.lib.vutbr.cz/wos/woscc/full-record/WOS:001135266200001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.9851" target="_blank" >10.1002/mma.9851</a>

Result language
angličtina
Original language name
Ground states of weighted 4D biharmonic equations with exponential growth
Original language description
In this paper, we are concerned with the existence of a ground state solution for a logarithmic weighted biharmonic equation under Dirichlet boundary conditions in the unit ball B$$ B $$ of Double-struck capital R4$$ {mathrm{mathbb{R}}} circumflex 4 $$. The reaction term of the equation is assumed to have exponential growth, in view of Adams' type inequalities. It is proved that there is a ground state solution using min-max techniques and the Nehari method. The associated energy functional loses compactness at a certain level. An appropriate asymptotic condition allows us to bypass the non-compactness levels of the functional.
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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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