scholarly journals On the development of nonlinear operator theory

2020 ◽  
Vol 54 (1) ◽  
pp. 63-68
Author(s):  
Вэньcян Вэй ◽  
WenHsiang Wei
Keyword(s):  
Operator Theory ◽  
Nonlinear Operator

Приведены основные результаты для нелинейных операторов. Эти результаты включают нелинейные версии классических теорем: теоремы о равномерной ограниченности и теоремы Хана-Банаха. Кроме того, показано, что отображения метризуемого пространства в нормированное пространство могут лежать в некоторых нормированных пространствах при подходящем определении норм.

scholarly journals An algorithm for finding common solutions of various problems in nonlinear operator theory

2014 ◽  
Vol 2014 (1) ◽  
pp. 9 ◽  
Author(s):  
Eric U Ofoedu ◽  
Jonathan N Odumegwu ◽  
Habtu Zegeye ◽  
Naseer Shahzad
Keyword(s):  
Operator Theory ◽  
Nonlinear Operator

scholarly journals Some elementary examples in nonlinear operator theory

2000 ◽  
Vol 32 (11-13) ◽  
pp. 1367-1376
Author(s):  
J. Appell ◽  
P.P. Zabrejko
Keyword(s):  
Operator Theory ◽  
Nonlinear Operator

scholarly journals Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jamal H. Al-Smail ◽  
Salim A. Messaoudi ◽  
Ala A. Talahmeh
Keyword(s):  
Parabolic Equation ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Nonlinear Operator ◽  
Numerical Study ◽  
Well Posedness ◽  
Two Dimensional ◽  
Nonlinear Parabolic ◽  
Decay Of Solutions

We consider the following nonlinear parabolic equation: ut-div(|∇u|p(x)-2∇u)=f(x,t), where f:Ω×(0,T)→R and the exponent of nonlinearity p(·) are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions.

scholarly journals Onξ(s)-Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov ◽  
Izzat Qaralleh
Keyword(s):  
Time Evolution ◽  
General Problem ◽  
Operator Theory ◽  
Nonlinear Operator ◽  
Two Dimensional ◽  
Dimensional Simplex ◽  
Nonlinear Operators ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We studyξ(s)-QSO defined on 2D simplex. We first classifyξ(s)-QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.

scholarly journals Nonlinear Operator Theory and Its Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-2
Author(s):  
Juan Martinez-Moreno ◽  
Dhananjay Gopal ◽  
Vijay Gupta ◽  
Edixon Rojas ◽  
Satish Shukla
Keyword(s):  
Operator Theory ◽  
Nonlinear Operator
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