scholarly journals Existence and nonexistence of positive radial solutions for a class of $p$-Laplacian superlinear problems with nonlinear boundary conditions

2020 ◽  
Vol 19 (9) ◽  
pp. 4655-4666
Author(s):  
Trad Alotaibi ◽  
◽  
D. D. Hai ◽  
R. Shivaji ◽  
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Radial Solutions ◽  
Positive Radial Solutions ◽  
Existence And Nonexistence

Existence of positive radial solutions for a superlinear semipositone p-Laplacian problem on the exterior of a ball

2018 ◽  
Vol 148 (2) ◽  
pp. 409-428 ◽  
Author(s):  
Quinn Morris ◽  
Ratnasingham Shivaji ◽  
Inbo Sim
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Nonlinear Boundary ◽  
A Priori ◽  
Nonlinear Boundary Conditions ◽  
Radial Solutions ◽  
Existence Of A Solution ◽  
Positive Radial Solutions

We prove the existence of positive radial solutions to a class of semipositone p-Laplacian problems on the exterior of a ball subject to Dirichlet and nonlinear boundary conditions. Using variational methods we prove the existence of a solution, and then use a priori estimates to prove the positivity of the solution.

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