scholarly journals An open mapping theorem for nonlinear operator equations associated with elliptic complexes

2021 ◽  
pp. 1-23
Author(s):  
Alexander Polkovnikov
Keyword(s):  
Nonlinear Operator ◽  
Open Mapping ◽  
Operator Equations ◽  
Open Mapping Theorem ◽  
Nonlinear Operator Equations ◽  
Elliptic Complexes

scholarly journals Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

1986 ◽  
Vol 9 (3) ◽  
pp. 583-587
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

The Existence of Solutions for Nonlinear Operator Equations

2008 ◽  
Vol 15 (1) ◽  
pp. 45-52
Author(s):  
Marek Galewski
Keyword(s):  
Nonlinear Operator ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Nonlinear Operator Equation ◽  
Global Minima ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Dual Variational Method ◽  
Dual Action ◽  
Primal And Dual

Abstract We provide the existence results for a nonlinear operator equation Λ*Φ′ (Λ𝑥) = 𝐹′(𝑥), in case 𝐹 – Φ is not necessarily convex. We introduce the dual variational method which is based on finding global minima of primal and dual action functionals on certain nonlinear subsets of their domains and on investigating relations between the minima obtained. The solution is a limit of a minimizng sequence whose existence and convergence are proved. The application for the non-convex Dirichlet problem with P.D.E. is given.

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