scholarly journals Existence of infinitely many radial nodal solutions for a Dirichlet problem involving mean curvature operator in Minkowski space

2020 ◽  
pp. 1-14
Author(s):  
Man Xu ◽  
Ruyun Ma
Keyword(s):  
Dirichlet Problem ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Nodal Solutions ◽  
Mean Curvature Operator

scholarly journals Nodal Solutions for Problems with Mean Curvature Operator in Minkowski Space with Nonlinearity Jumping Only at the Origin

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wenguo Shen
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Global Bifurcation ◽  
Connected Components ◽  
Curvature Operator ◽  
Linear Perturbation ◽  
Open Ball ◽  
Nodal Solutions ◽  
Mean Curvature Operator ◽  
Perturbation Problems

In this paper, we establish a unilateral global bifurcation result for half-linear perturbation problems with mean curvature operator in Minkowski space. As applications of the abovementioned result, we shall prove the existence of nodal solutions for the following problem −div∇v/1−∇v2=αxv++βxv−+λaxfv, in BR0,vx=0, on ∂BR0, where λ ≠ 0 is a parameter, R is a positive constant, and BR0=x∈ℝN:x<R is the standard open ball in the Euclidean space ℝNN≥1 which is centered at the origin and has radius R. a(|x|) ∈ C[0, R] is positive, v+ = max{v, 0}, v− = −min{v, 0}, α(|x|), β(|x|) ∈ C[0, R]; f∈Cℝ,ℝ, s f (s) > 0 for s ≠ 0, and f0 ∈ [0, ∞], where f0 = lim|s|⟶0 f(s)/s. We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.

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.

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