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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Multiplicity results for a subcritical Hamiltonian system with concave-convex nonlinearities
Original language description
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>0,v>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 > 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(& lowast;)(mu) on an interval [0, mu] with lambda(& lowast;)(0) > 0, lambda(& 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.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA22-18261S" target="_blank" >GA22-18261S: Nonlinear problems with non-standard diffusion</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

Name of the periodical
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN
0944-2669
e-ISSN
1432-0835
Volume of the periodical
64
Issue of the periodical within the volume
9
Country of publishing house
DE - GERMANY
Number of pages
40
Pages from-to
1-40
UT code for WoS article
001592839300023
EID of the result in the Scopus database
2-s2.0-105018709023

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