Structure of least-energy solutions for quasilinear elliptic equations on convex domains

2008 ◽  
Vol 68 (8) ◽  
pp. 2349-2356
Author(s):  
Zhengce Zhang ◽  
Liping Zhu ◽  
Kaitai Li
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Convex Domains ◽  
Least Energy Solutions ◽  
Quasilinear Elliptic ◽  
Least Energy

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

2019 ◽  
Vol 149 (5) ◽  
pp. 1163-1173
Author(s):  
Vladimir Bobkov ◽  
Sergey Kolonitskii
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Quasilinear Elliptic Equations ◽  
Nodal Set ◽  
Sign Changing Solutions ◽  
Quasilinear Elliptic ◽  
Least Energy

AbstractIn 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 nodal set of any least energy sign-changing solution intersects the boundary of Ω. The proof is based on a moving polarization argument.

Existence of a Least Energy Nodal Solution for a Class of p&q-Quasilinear Elliptic Equations

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
Sara Barile ◽  
Giovany M. Figueiredo
Keyword(s):  
Bounded Domain ◽  
Elliptic Equations ◽  
Existence Result ◽  
Quasilinear Elliptic Equations ◽  
Nodal Solution ◽  
Smooth Bounded Domain ◽  
Quasilinear Elliptic ◽  
Least Energy

AbstractIn this paper we prove an existence result for a least energy nodal (or sign-changing) solution for the class of p&q problems given bywhere Ω is a smooth bounded domain in ℝ

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