scholarly journals Uniqueness of the Positive Radial Solution on an Annulus of the Dirichlet Problem forΔu−u+u3=0

1996 ◽  
Vol 128 (2) ◽  
pp. 379-386 ◽  
Author(s):  
Charles V. Coffman
Keyword(s):  
Dirichlet Problem ◽  
Radial Solution ◽  
Positive Radial Solution

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.

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
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