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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