On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

  title={On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations},
  author={Vladimir Bobkov and Sergey Kolonitskii},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  pages={1163 - 1173}
  • V. Bobkov, S. Kolonitskii
  • Published 10 July 2017
  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Abstract 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 {{\open 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 Ω. We show that the… 
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