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 Existence of Positive Solutions of One-Dimensional Prescribed Mean Curvature Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Ruyun Ma ◽  
Lingfang Jiang
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
Quadrature Method ◽  
One Dimensional ◽  
Curvature Equation ◽  
Exact Number ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Equation ◽  
Prescribed Mean Curvature Equation ◽  
Existence Of Positive Solutions

We consider the existence of positive solutions of one-dimensional prescribed mean curvature equation−(u′/1+u′2)′=λf(u),0<t<1,u(t)>0,t∈(0,1),u(0)=u(1)=0whereλ>0is a parameter, andf:[0,∞)→[0,∞)is continuous. Further, whenfsatisfiesmax{up,uq}≤f(u)≤up+uq,0<p≤q<+∞, we obtain the exact number of positive solutions. The main results are based upon quadrature method.

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