Normalized solutions for (p,q)-Laplacian equations with mass supercritical growth

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F24%3APU151072" target="_blank" >RIV/00216305:26220/24:PU151072 - isvavai.cz</a>
Result on the web
<a href="https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0022039624000536?via%3Dihub" target="_blank" >https://www-sciencedirect-com.ezproxy.lib.vutbr.cz/science/article/pii/S0022039624000536?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2024.01.041" target="_blank" >10.1016/j.jde.2024.01.041</a>

Result language
angličtina
Original language name
Normalized solutions for (p,q)-Laplacian equations with mass supercritical growth
Original language description
In this paper, we study the following (p,q)-Laplacian equation with Lp-constraint: {−Δpu−Δqu+λ|u|p−2u=f(u),inRN,∫R|u|pdx=cp,u∈W1,p(RN)∩W1,q(RN), where 1<p<q<N, Δi=div(|∇u|i−2∇u), with i∈{p,q}, is the i-Laplacian operator, λ is a Lagrange multiplier and c>0 is a constant. The nonlinearity f is assumed to be continuous and satisfying weak mass supercritical conditions. The purpose of this paper is twofold: to establish the existence of ground states, and to reveal the basic behavior of the ground state energy Ec as c>0 varies. Moreover, we introduce a new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints intersected with the closed ball of radius cp in Lp(RN). The analysis developed in this paper allows to provide the general growth assumptions imposed to the reaction f.
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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