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

@article{Bobkov2019OnAP, 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}, year={2019}, volume={149}, pages={1163 - 1173} }

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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