Positive rotationally symmetric solutions for a Dirichlet problem involving the higher mean curvature operator in Minkowski space

2018 ◽  
Vol 460 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Ruyun Ma ◽  
Man Xu
Keyword(s):  
Dirichlet Problem ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Rotationally Symmetric ◽  
Mean Curvature Operator

The Dirichlet Problem with Mean Curvature Operator in Minkowski Space – a Variational Approach

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
C. Bereanu ◽  
P. Jebelean ◽  
J. Mawhin
Keyword(s):  
Dirichlet Problem ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Variational Approach ◽  
Curvature Operator ◽  
Mean Curvature Operator

AbstractIn this paper we consider the Dirichlet problem with mean curvature operator in Minkowski space :where Ω ⊂ ℝ

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.

Nontrivial Solutions for Potential Systems Involving the Mean Curvature Operator in Minkowski Space

2017 ◽  
Vol 17 (4) ◽  
pp. 769-780 ◽  
Author(s):  
Daniela Gurban ◽  
Petru Jebelean ◽  
Călin Şerban
Keyword(s):  
Minkowski Space ◽  
Critical Point Theory ◽  
Mean Curvature ◽  
Lower Semicontinuous ◽  
Point Theory ◽  
Curvature Operator ◽  
Nontrivial Solutions ◽  
Potential System ◽  
Mean Curvature Operator ◽  
The Mean

AbstractIn this paper, we use the critical point theory for convex, lower semicontinuous perturbations of{C^{1}}-functionals to obtain the existence of multiple nontrivial solutions for one parameter potential systems involving the operator{u\mapsto\operatorname{div}(\frac{\nabla u}{\sqrt{1-|\nabla u|^{2}}})}. The solvability of a general non-potential system is also established.

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