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 Fixed Point Theorems for Generalized αs-ψ-Contractions with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Zhenhua Ma ◽  
Muhammad Nazam ◽  
Sami Ullah Khan ◽  
Xiangling Li
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Elliptic Boundary ◽  
Sufficient Conditions ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Unique Common Fixed Point

We study the sufficient conditions for the existence of a unique common fixed point of generalized αs-ψ-Geraghty contractions in an αs-complete partial b-metric space. We give an example in support of our findings. Our work generalizes many existing results in the literature. As an application of our findings we demonstrate the existence of the solution of the system of elliptic boundary value problems.

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