GROUND STATES OF BIHARMONIC EQUATIONS ON LATTICE GRAPHS

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

GROUND STATES OF BIHARMONIC EQUATIONS ON LATTICE GRAPHS

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

GROUND STATES OF BIHARMONIC EQUATIONS ON LATTICE GRAPHS

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Topological Methods in Nonlinear Analysis

ISSN

1230-3429

e-ISSN

—

Svazek periodika

66

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

16

Strana od-do

273-288

Kód UT WoS článku

001651329000013

EID výsledku v databázi Scopus

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