scholarly journals Existence of positive radial solution for Neumann problem on the Heisenberg group

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
F. Safari ◽  
A. Razani
Keyword(s):  
Heisenberg Group ◽  
Neumann Problem ◽  
Radial Solution ◽  
Positive Radial Solution

scholarly journals Existence of the second positive radial solution for a p-Laplacian problem

2011 ◽  
Vol 235 (13) ◽  
pp. 3743-3750 ◽  
Author(s):  
Chan-Gyun Kim ◽  
Eun Kyoung Lee ◽  
Yong-Hoon Lee
Keyword(s):  
Radial Solution ◽  
Positive Radial Solution

The Explicit Solution of the -Neumann Problem in a Non-Isotropic Siegel Domain

1997 ◽  
Vol 49 (6) ◽  
pp. 1299-1322 ◽  
Author(s):  
Jingzhi Tie
Keyword(s):  
Differential Equation ◽  
Fundamental Solution ◽  
Heat Equation ◽  
Heisenberg Group ◽  
Neumann Problem ◽  
Explicit Solution ◽  
Laplacian Operator ◽  
Siegel Domain ◽  
The Neumann Problem ◽  
Image Position

AbstractIn this paper, we solve the-Neumann problem on (0, q) forms, 0 ≤ q ≤ n, in the strictly pseudoconvex non-isotropic Siegel domain:where aj> 0 for j = 1,2, . . . , n. The metric we use is invariant under the action of the Heisenberg group on the domain. The fundamental solution of the related differential equation is derived via the Laguerre calculus. We obtain an explicit formula for the kernel of the Neumann operator. We also construct the solution of the corresponding heat equation and the fundamental solution of the Laplacian operator on the Heisenberg group.

The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍ n $\mathbb H_{n}$

2016 ◽  
Vol 45 (1) ◽  
pp. 119-133 ◽  
Author(s):  
Shivani Dubey ◽  
Ajay Kumar ◽  
Mukund Madhav Mishra
Keyword(s):  
Heisenberg Group ◽  
Neumann Problem ◽  
Kohn Laplacian ◽  
The Neumann Problem

scholarly journals Existence of radial solutions for a $p(x)$-Laplacian Dirichlet problem

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Maria Alessandra Ragusa ◽  
Abdolrahman Razani ◽  
Farzaneh Safari
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Variational Methods ◽  
Unit Ball ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Radial Solution ◽  
Radial Solutions ◽  
Positive Radial Solution ◽  
Radial Functions

AbstractIn this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized $p(x)$ p ( x ) -Laplacian problem $$ -\Delta _{p(x)} u + R(x) u^{p(x)-2}u=a (x) \vert u \vert ^{q(x)-2} u- b(x) \vert u \vert ^{r(x)-2} u $$ − Δ p ( x ) u + R ( x ) u p ( x ) − 2 u = a ( x ) | u | q ( x ) − 2 u − b ( x ) | u | r ( x ) − 2 u with Dirichlet boundary condition in the unit ball in $\mathbb{R}^{N}$ R N (for $N \geq 3$ N ≥ 3 ), where a, b, R are radial functions.

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