scholarly journals MULTIPLE POSITIVE SOLUTIONS OF THE DISCRETE DIRICHLET PROBLEM WITH ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE OPERATOR

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Yanqiong Lu ◽  
◽  
Ruyun Ma
Keyword(s):  
Dirichlet Problem ◽  
Positive Solutions ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Multiple Positive Solutions ◽  
One Dimensional ◽  
Prescribed Mean Curvature ◽  
Mean Curvature Operator

scholarly journals Positive solutions of the discrete Dirichlet problem involving the mean curvature operator

2019 ◽  
Vol 17 (1) ◽  
pp. 1055-1064 ◽  
Author(s):  
Jiaoxiu Ling ◽  
Zhan Zhou
Keyword(s):  
Dirichlet Problem ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Mean Curvature ◽  
Nonlinear Term ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Curvature Operator ◽  
Mean Curvature Operator ◽  
The Mean

Abstract In this paper, by using critical point theory, we obtain some sufficient conditions on the existence of infinitely many positive solutions of the discrete Dirichlet problem involving the mean curvature operator. We show that the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a sequence of pairwise distinct nontrivial positive solutions. We also give two examples to illustrate our main results.

Positive Solutions for BVPs with One-dimensional Mean Curvature Operator

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
João Marcos do Ó ◽  
Aleksandra Orpel
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Dirichlet Problems ◽  
One Dimensional ◽  
Functional Parameters ◽  
Mean Curvature Operator

AbstractWe discuss the existence and properties of solutions for systems of Dirichlet problems involving one dimensional mean curvature operator. Our approach is based on variational methods and covers both sublinear and superlinear cases of nonlinearities. We also investigate the continuous (in some sense) dependence of solutions on functional parameters.

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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