Semilinear elliptic equations involving power nonlinearities and Hardy potentials with boundary singularities

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144214" target="_blank" >RIV/00216224:14310/25:00144214 - isvavai.cz</a>

Result on the web

<a href="https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/semilinear-elliptic-equations-involving-power-nonlinearities-and-hardy-potentials-with-boundary-singularities/1FA7BF7DD7DB916CFDAC66C169C4" target="_blank" >https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/semilinear-elliptic-equations-involving-power-nonlinearities-and-hardy-potentials-with-boundary-singularities/1FA7BF7DD7DB916CFDAC66C169C4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/prm.2023.122" target="_blank" >10.1017/prm.2023.122</a>

Result language

angličtina

Original language name

Semilinear elliptic equations involving power nonlinearities and Hardy potentials with boundary singularities

Original language description

Let Ω ⊂ RN (N ≽ 3) be a C2 bounded domain and Σ ⊂ ∂Ω be a C2 compact submanifold without boundary, of dimension k, 0 ≼ k ≼ N - 1. We assume that Σ = {0} if k = 0 and Σ = ∂Ω if k = N - 1. Let dΣ(x) = dist (x, Σ) and Lμ = Δ + μ d-Σ2, where μ ∈ R. We study boundary value problems (P±) -Lμu ± |u|p-1u = 0 in Ω and trμ,Σ(u) = ν on ∂Ω, where p &gt; 1, ν is a given measure on ∂Ω and trμ,Σ(u) denotes the boundary trace of u associated to Lμ. Different critical exponents for the existence of a solution to (P±) appear according to concentration of ν. The solvability for problem (P+) was proved in [3, 29] in subcritical ranges for p, namely for p smaller than one of the critical exponents. In this paper, assuming the positivity of the first eigenvalue of -Lμ, we provide conditions on ν expressed in terms of capacities for the existence of a (unique) solution to (P+) in supercritical ranges for p, i.e. for p equal or bigger than one of the critical exponents. We also establish various equivalent criteria for the existence of a solution to (P-) under a smallness assumption on ν.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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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

2025

Confidentiality

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

Name of the periodical

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

ISSN

0308-2105

e-ISSN

1473-7124

Volume of the periodical

155

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

58

Pages from-to

993-1050

UT code for WoS article

001133169600001

EID of the result in the Scopus database

2-s2.0-85180930351