GROUND STATES OF BIHARMONIC EQUATIONS ON LATTICE GRAPHS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F26%3A0200226" target="_blank" >RIV/00216305:26220/26:0200226 - isvavai.cz</a>
Result on the web
<a href="https://www.tmna.ncu.pl/static/published/2025/v66n1-13.pdf" target="_blank" >https://www.tmna.ncu.pl/static/published/2025/v66n1-13.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.12775/TMNA.2025.014" target="_blank" >10.12775/TMNA.2025.014</a>

Result language
angličtina
Original language name
GROUND STATES OF BIHARMONIC EQUATIONS ON LATTICE GRAPHS
Original language description
In this paper, we are concerned with the existence of ground states to the following biharmonic equation on the lattice graph Delta 2u-Delta u +V(x)u= f(x,u), x is an element of ZN. The analysis is performed if the potential V and the reaction f are Tperiodic in x, and the mapping u 7 -> f (x, u)/u is non-decreasing on R{0}. By using the variational methods, we establish the existence of ground states for the above problem. Moreover, if the potential V has a bounded potential well and f (x, u) = f (u) with u 7 -> f(u)/u non-decreasing on R {0}, the ground states are also obtained for the above equation. Finally, we extend the main results on the lattice graph ZN to quasi-transitive graphs. In our analysis, the mappings u 7 -> f (x, u)/u or u 7 -> f(u)/uare only non-decreasing on R {0}, which allows to consider larger classes of nonlinearities in the reaction.
Czech name
—
Czech description
—

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

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)