Bifurcation of nodal radial solutions for a prescribed mean curvature problem on an exterior domain

2020 ◽  
Vol 268 (8) ◽  
pp. 4464-4490 ◽  
Author(s):  
Rui Yang ◽  
Yong-Hoon Lee ◽  
Inbo Sim
Keyword(s):  
Mean Curvature ◽  
Exterior Domain ◽  
Radial Solutions ◽  
Prescribed Mean Curvature ◽  
Curvature Problem

Radial Solutions of the Dirichlet Problem for the Prescribed Mean Curvature Equation in a Robertson-Walker Spacetime

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Daniel de la Fuente ◽  
Alfonso Romero ◽  
Pedro J. Torres
Keyword(s):  
Fixed Point ◽  
Mean Curvature ◽  
Existence Result ◽  
Euclidean Ball ◽  
Radial Solutions ◽  
Curvature Equation ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equation ◽  
Prescribed Mean Curvature Equation ◽  
Curvature Problem

AbstractWe consider the prescribed mean curvature problem of spacelike graphs in Robertson- Walker spacetimes of flat fiber with homogeneous Dirichlet conditions on an Euclidean ball. Under reasonable assumptions, it is shown that every possible solution must be radially symmetric. Besides, an existence result for a singular nonlinear equation is proved by making use of the classical Schauder fixed point Theorem. The results are applied to realistic examples of Robertson-Walker spacetimes.

Positive Solutions of an Indefinite Prescribed Mean Curvature Problem on a General Domain

2004 ◽  
Vol 4 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Patrick Habets ◽  
Pierpaolo Omari
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
General Domain ◽  
Prescribed Mean Curvature ◽  
Existence Of Positive Solutions ◽  
Curvature Problem

AbstractThe existence of positive solutions is proved for the prescribed mean curvature problemwhere Ω ⊂ℝ

scholarly journals Revisiting the sub- and super-solution method for the classical radial solutions of the mean curvature equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1185-1205
Author(s):  
Franco Obersnel ◽  
Pierpaolo Omari
Keyword(s):  
Mean Curvature ◽  
Solution Method ◽  
The Novel ◽  
Open Ball ◽  
Radial Solutions ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
Radially Symmetric Solutions ◽  
The Mean ◽  
Curvature Problem

Abstract This paper focuses on the existence and the multiplicity of classical radially symmetric solutions of the mean curvature problem: \left\{\begin{array}{ll}-\text{div}\left(\frac{\nabla v}{\sqrt{1+|\nabla v{|}^{2}}}\right)=f(x,v,\nabla v)& \text{in}\hspace{.5em}\text{Ω},\\ {a}_{0}v+{a}_{1}\tfrac{\partial v}{\partial \nu }=0& \text{on}\hspace{.5em}\partial \text{Ω},\end{array}\right. with \text{Ω} an open ball in {{\mathbb{R}}}^{N} , in the presence of one or more couples of sub- and super-solutions, satisfying or not satisfying the standard ordering condition. The novel assumptions introduced on the function f allow us to complement or improve several results in the literature.

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