Nonlinear noncoercive operator equations and their regularization in banach spaces

1997 ◽  
Vol 33 (3) ◽  
pp. 409-415
Author(s):  
D. E. Akbarov
Keyword(s):  
Banach Spaces ◽  
Operator Equations

scholarly journals Iterative Solution for Systems of a Class of Abstract Operator Equations in Banach Spaces and Application

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hua Su
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Iterative Solution ◽  
Order Method ◽  
Operator Equations ◽  
Abstract Operator ◽  
Uniqueness Of A Solution

In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.

scholarly journals Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yonghui Ling ◽  
Xiubin Xu ◽  
Shaohua Yu
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Nonlinear Operator ◽  
Convergence Criterion ◽  
Second Derivative ◽  
Operator Equations ◽  
Convergence Ball ◽  
Nonlinear Operator Equations ◽  
Steffensen’S Method ◽  
Convergence Problems

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.

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 Nonlinear random operator equations and inequalities in Banach spaces

1992 ◽  
Vol 15 (1) ◽  
pp. 111-118 ◽  
Author(s):  
Antonios Karamolegos ◽  
Dimitrios Kravvaritis
Keyword(s):  
Banach Spaces ◽  
Existence Theorems ◽  
Random Operator ◽  
Measurable Selection ◽  
Hammerstein Integral Equation ◽  
Operator Equations ◽  
Deterministic Theory ◽  
Measurable Multifunctions ◽  
Selection Theorems ◽  
Monotone Type

In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable multifunctions and, in particular, the measurable selection theorems of Kuratowski/Ryll-Nardzewski and of Saint-Beuve.

Sign in / Sign up

Export Citation Format

Share Document