High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139428" target="_blank" >RIV/00216224:14310/24:00139428 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s12220-024-01637-2" target="_blank" >https://link.springer.com/article/10.1007/s12220-024-01637-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s12220-024-01637-2" target="_blank" >10.1007/s12220-024-01637-2</a>

Result language
angličtina
Original language name
High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity
Original language description
This article deals with the study of the following Kirchhoff-Choquard problem: begin{equation*} begin{array}{cc} displaystyle Mleft(, intlimits_{mathbb{R}^N}|nabla u|^pright) (-Δ_p) u + V(x)|u|^{p-2}u = left(, intlimits_{mathbb{R}^N}frac{F(u)(y)}{|x-y|^μ},dy right) f(u), ;;text{in} ; mathbb{R}^N, u > 0, ;; text{in} ; mathbb{R}^N, end{array} end{equation*} where $M$ models Kirchhoff-type nonlinear term of the form $M(t) = a + bt^{θ-1}$, where $a, b > 0$ are given constants; $1<p<N$, $Δ_p = text{div}(|nabla u|^{p-2}nabla u)$ is the $p$-Laplacian operator; potential $V in C^2(mathbb{R}^N)$; $f$ is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for $θin left[1, frac{2N-μ}{N-p}right) $ via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem.
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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