Boundary-Value Problems with Control for Operator Equations in Banach Spaces

2021 ◽  
Author(s):  
O. A. Boichuk ◽  
V. P. Zhuravliov
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Boundary Value ◽  
Operator Equations

scholarly journals Nonlinear Sum Operator Equations with a Parameter and Application to Second-Order Three-Point BVPs

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wen-Xia Wang ◽  
Xi-Lan Liu ◽  
Piao-Piao Shi
Keyword(s):  
Nonlinear Analysis ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Critical Value ◽  
Second Order ◽  
Point Boundary ◽  
Operator Equations

A class of nonlinear sum operator equations with a parameter on order Banach spaces were considered. The existence and uniqueness of positive solutions for this kind of operator equations and the dependence of solutions on the parameter have been obtained by using the properties of cone and nonlinear analysis methods. The critical value of the parameter was estimated. Further, the application to some nonlinear three-point boundary value problems was given to show the significance of the discussion.

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

Sign in / Sign up

Export Citation Format

Share Document