Fixed Points in Ordered Banach Spaces and Applications to Elliptic Boundary-Value Problems

2006 ◽  
pp. 25-31 ◽  
Author(s):  
Gabriele Bonanno ◽  
Salvatore Marano
Keyword(s):  
Fixed Points ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Ordered Banach Spaces

scholarly journals Nonnegative Solutions of a Nonlinear System and Applications to Elliptic BVPs*

2021 ◽  
pp. 15-26
Author(s):  
Guangchong Yang ◽  
Yanqiu Chen
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonnegative Solutions

Abstract In this communication, we study the existence of nonnegative solutions of a nonlinear system in Banach spaces. These maps involved in the system defined on cone do not necessarily take values in the cone. Using fixed point theorems just established for this type of mappings, nonnegative solutions of the system are obtained and used to investigate elliptic boundary value problems (BVPs). MSC(2010): 47H10, 35J57. Keywords: Nonlinear system, Nonnegative solutions, Nowhere normal-outward maps, Fixed point, Elliptic BVPs.

scholarly journals Multiplicity of positive solutions to semilinear elliptic boundary value problems

1999 ◽  
Vol 4 (3) ◽  
pp. 195-208
Author(s):  
Kenichiro Umezu
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Degree Theory ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions ◽  
Ordered Banach Spaces

We study semilinear elliptic boundary value problems of one parameter dependence where the number of positive solutions is discussed. Our main purpose is to characterize the critical value given by the infimum of such parameters for which positive solutions exist. Our approach is based on super- and sub-solutions, and relies on the topological degree theory on the positive cones of ordered Banach spaces. A concrete example is also presented.

Sign in / Sign up

Export Citation Format

Share Document