On the solvability of nonlinear equations involving abstract and differential operators

1979 ◽  
pp. 209-247 ◽  
Author(s):  
W. V. Petryshyn
Keyword(s):  
Nonlinear Equations ◽  
Differential Operators

Nonlinear equations with essentially infinite-dimensional differential operators

2011 ◽  
Vol 62 (11) ◽  
pp. 1822-1827
Author(s):  
Yu. V. Bohdans’kyi ◽  
V. M. Statkevych
Keyword(s):  
Nonlinear Equations ◽  
Differential Operators ◽  
Infinite Dimensional

scholarly journals Formal Pseudodifferential Operators in One and Several Variables, Central Extensions, and Integrable Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Jarnishs Beltran ◽  
Enrique G. Reyes
Keyword(s):  
Lie Algebras ◽  
Nonlinear Equations ◽  
Integrable Systems ◽  
Differential Operators ◽  
Pseudodifferential Operators ◽  
Central Extensions ◽  
Several Variables ◽  
Zero Curvature ◽  
Manin Triples

We review some aspects of the theory of Lie algebras of (twisted and untwisted) formal pseudodifferential operators in one and several variables in a general algebraic context. We focus mainly on the construction and classification of nontrivial central extensions. As applications, we construct hierarchies of centrally extended Lie algebras of formal differential operators in one and several variables, Manin triples and hierarchies of nonlinear equations in Lax and zero curvature form.

Recognition of Signals with Application of Nonlinear Equations of Dynamics

1999 ◽  
Vol 31 (12) ◽  
pp. 81-87
Author(s):  
Tatyana I. Aksenova ◽  
Igor V. Tetko
Keyword(s):  
Nonlinear Equations

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
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