Multiplicity results for a subcritical Hamiltonian system with concave-convex nonlinearities

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43978353" target="_blank" >RIV/49777513:23520/25:43978353 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00526-025-03094-3" target="_blank" >https://link.springer.com/article/10.1007/s00526-025-03094-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00526-025-03094-3" target="_blank" >10.1007/s00526-025-03094-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multiplicity results for a subcritical Hamiltonian system with concave-convex nonlinearities

Popis výsledku v původním jazyce

We study the Hamiltonian elliptic system { -Delta u=lambda|v|(r-1)v+|v|(p-1)v in Omega, -Delta v=mu|u|(s-1)u+|u|(q-1)u in Omega, (0.1) u&gt;0,v&gt;0 in Omega u=v=0 on partial derivative Omega where Omega subset of R-N is a smooth bounded domain, lambda and mu are nonnegative parameters and r, s, p, q &gt; 0. Our study includes the case in which the nonlinearities in (0.1) are concave near the origin and convex near infinity, and we focus on the region of non-negative pairs of parameters(lambda, mu) that guarantee existence and multiplicity of solutions of (0.1). In particular, we show the existence of a strictly decreasing curve lambda(&amp; lowast;)(mu) on an interval [0, mu] with lambda(&amp; lowast;)(0) &gt; 0, lambda(&amp; lowast;)(mu) = 0 and such that the system has two solutions for (lambda, mu) below the curve, one solution for (lambda, mu) on the curve and no solution for (lambda, mu) above the curve. A similar statement holds reversing lambda and mu.

Název v anglickém jazyce

Multiplicity results for a subcritical Hamiltonian system with concave-convex nonlinearities

Popis výsledku anglicky

We study the Hamiltonian elliptic system { -Delta u=lambda|v|(r-1)v+|v|(p-1)v in Omega, -Delta v=mu|u|(s-1)u+|u|(q-1)u in Omega, (0.1) u&gt;0,v&gt;0 in Omega u=v=0 on partial derivative Omega where Omega subset of R-N is a smooth bounded domain, lambda and mu are nonnegative parameters and r, s, p, q &gt; 0. Our study includes the case in which the nonlinearities in (0.1) are concave near the origin and convex near infinity, and we focus on the region of non-negative pairs of parameters(lambda, mu) that guarantee existence and multiplicity of solutions of (0.1). In particular, we show the existence of a strictly decreasing curve lambda(&amp; lowast;)(mu) on an interval [0, mu] with lambda(&amp; lowast;)(0) &gt; 0, lambda(&amp; lowast;)(mu) = 0 and such that the system has two solutions for (lambda, mu) below the curve, one solution for (lambda, mu) on the curve and no solution for (lambda, mu) above the curve. A similar statement holds reversing lambda and mu.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-18261S" target="_blank" >GA22-18261S: Nelineární úlohy s nestandardní difuzí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

ISSN

0944-2669

e-ISSN

1432-0835

Svazek periodika

64

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

40

Strana od-do

1-40

Kód UT WoS článku

001592839300023

EID výsledku v databázi Scopus

2-s2.0-105018709023