Multiplicity and concentration of solutions to fractional anisotropic Schrodinger equations with exponential growth
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F23%3APU148505" target="_blank" >RIV/00216305:26220/23:PU148505 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00229-022-01450-7" target="_blank" >https://link.springer.com/article/10.1007/s00229-022-01450-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00229-022-01450-7" target="_blank" >10.1007/s00229-022-01450-7</a>
Alternative languages
Result language
angličtina
Original language name
Multiplicity and concentration of solutions to fractional anisotropic Schrodinger equations with exponential growth
Original language description
In this paper, we consider the Schrodinger equation involving the fractional $(p, p_1, . . . , p_m)$-Laplacian as follows $(-Delta)_p^s u +sum_ {i=1}^m (-Delta)_{p_i}^s u + V(epsilon x)(|u|^{(N-2s)/2s} u + sum_{i=1}^m |u|^{p_i-2} u) = f (u) in R^N$ where $epsilon$ is a positive parameter, $N=ps, s in (0,1), 2 leq p < p_1 < dots < p_m < +infty, m geq 1$. The nonlinear function f has the exponential growth and potential function V is continuous function satisfying some suitable conditions. Using the penalization method and Ljusternik-Schnirelmann theory, we study the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter. In our best knowledge, it is the first time that the above problem is studied.
Czech name
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Czech description
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Classification
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
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MANUSCRIPTA MATHEMATICA
ISSN
0025-2611
e-ISSN
1432-1785
Volume of the periodical
173
Issue of the periodical within the volume
1-2
Country of publishing house
DE - GERMANY
Number of pages
56
Pages from-to
499-554
UT code for WoS article
000922764800001
EID of the result in the Scopus database
2-s2.0-85146845106