On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43956908" target="_blank" >RIV/49777513:23520/19:43956908 - 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/on-a-property-of-the-nodal-set-of-least-energy-signchanging-solutions-for-quasilinear-elliptic-equations/4CA30B15FD2F69CE720F0995084E5F14" target="_blank" >https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/on-a-property-of-the-nodal-set-of-least-energy-signchanging-solutions-for-quasilinear-elliptic-equations/4CA30B15FD2F69CE720F0995084E5F14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/prm.2018.88" target="_blank" >10.1017/prm.2018.88</a>
Alternative languages
Result language
angličtina
Original language name
On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations
Original language description
In this note, we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation -Delta(p)u = f(u) in bounded Steiner symmetric domains Omega subset of R-N under the zero Dirichlet boundary conditions. The nonlinearity f is assumed to be either superlinear or resonant. In the latter case, least energy sign-changing solutions are second eigenfunctions of the zero Dirichlet p-Laplacian in Omega. We show that the nodal set of any least energy sign-changing solution intersects the boundary of Omega. The proof is based on a moving polarization argument.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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
Result continuities
Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN
0308-2105
e-ISSN
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Volume of the periodical
149
Issue of the periodical within the volume
5
Country of publishing house
GB - UNITED KINGDOM
Number of pages
11
Pages from-to
1163-1173
UT code for WoS article
000487465600004
EID of the result in the Scopus database
2-s2.0-85060012777