Existence and Multiplicity Results for Nonlocal Lane-Emden Systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134083" target="_blank" >RIV/00216224:14310/23:00134083 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s40306-022-00485-y" target="_blank" >https://doi.org/10.1007/s40306-022-00485-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40306-022-00485-y" target="_blank" >10.1007/s40306-022-00485-y</a>

Result language
angličtina
Original language name
Existence and Multiplicity Results for Nonlocal Lane-Emden Systems
Original language description
In this work, we show the existence and multiplicity for the nonlocal Lane-Emden system of the form begin{array}{@{}rcl@{}} left{ begin{aligned} mathbb L u &= v^{p} + rho nu quad &&text{in } {varOmega}, mathbb L v &= u^{q} + sigma tau quad &&text{in } {varOmega}, u&=v = 0 quad &&text{on } partial {varOmega} text{ or in } {varOmega}^{c} text{ if applicable}, end{aligned} right. end{array} where {varOmega } subset mathbb {R}^{N} is a C2 bounded domain, mathbb L is a nonlocal operator, ν,τ are Radon measures on Ω, p,q are positive exponents, and ρ,σ > 0 are positive parameters. Based on a fine analysis of the interaction between the Green kernel associated with mathbb L, the source terms uq,vp and the measure data, we prove the existence of a positive minimal solution. Furthermore, by analyzing the geometry of Palais-Smale sequences in finite dimensional spaces given by the Galerkin type approximations and their appropriate uniform estimates, we establish the existence of a second positive solution, under a smallness condition on the positive parameters ρ,σ and superlinear growth conditions on source terms. The contribution of the paper lies on our unifying technique that is applicable to various types of local and nonlocal operators.
Czech name
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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/GA22-17403S" target="_blank" >GA22-17403S: Nonlinear Schrödinger equations and systems with singular potentials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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