Title: On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations
Authors: Bobkov, Vladimír
Kolonitskii, Sergey
Citation: BOBKOV, V., KOLONITSKII, S. On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations. Proceedings of the royal society of Edinburgh section a-matematics, 2019, roč. 149, č. 5, s. 1163-1173. ISSN 0308-2105.
Issue Date: 2019
Publisher: Cambridge University Press
Document type: článek
article
URI: 2-s2.0-85060012777
http://hdl.handle.net/11025/36212
ISSN: 0308-2105
Keywords in different language: p-Laplacian;superlinear;second eigenvalue;least energy nodal solution;nodal set;Payne conjecture;polarization.
Abstract in different language: 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.
Rights: Plný text není přístupný.
� Cambridge University Press
Appears in Collections:Články / Articles (NTIS)
OBD

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