scholarly journals Nonexistence of positive solutions of Neumann problems for elliptic inequalities of the mean curvature type

1997 ◽  
Vol 27 (2) ◽  
pp. 271-293 ◽  
Author(s):  
Hiroyuki Usami
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
Neumann Problems ◽  
The Mean ◽  
Curvature Type ◽  
Elliptic Inequalities

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.

Global Gradient Estimate of the Mean Curvature Type Equation

2021 ◽  
Vol 11 (06) ◽  
pp. 1130-1136
Author(s):  
玉苏普 阿迪莱•
Keyword(s):  
Mean Curvature ◽  
Type Equation ◽  
Gradient Estimate ◽  
The Mean ◽  
Curvature Type

On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems

2000 ◽  
Vol 52 (3) ◽  
pp. 522-538 ◽  
Author(s):  
Changfeng Gui ◽  
Juncheng Wei
Keyword(s):  
Mean Curvature ◽  
Variational Approach ◽  
Existence Of Solutions ◽  
Sphere Packing ◽  
Curvature Function ◽  
Bounded Smooth Domain ◽  
Neumann Problems ◽  
Subcritical Nonlinearity ◽  
The Mean ◽  
Bounded Smooth

AbstractWe consider the problemwhere Ω is a bounded smooth domain in RN, ε > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses multiple boundary spike solutions that concentrate, as ε approaches zero, at multiple critical points of the mean curvature function H(P), P ∈ ∂Ω. It is also proved that this equation has multiple interior spike solutions which concentrate, as ε → 0, at sphere packing points in Ω.In this paper, we prove the existence of solutions with multiple spikes both on the boundary and in the interior. The main difficulty lies in the fact that the boundary spikes and the interior spikes usually have different scales of error estimation. We have to choose a special set of boundary spikes to match the scale of the interior spikes in a variational approach.

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