scholarly journals A Nonlinear Differential Operator Series That Commutes with Any Function

1992 ◽  
Vol 23 (1) ◽  
pp. 209-221 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Differential Operator ◽  
Operator Series ◽  
Nonlinear Differential Operator

Rondo: Rank-order based nonlinear differential operator

1992 ◽  
Vol 25 (9) ◽  
pp. 1043-1059 ◽  
Author(s):  
Akira Asano ◽  
Kazuyoshi Itoh ◽  
Yoshiki Ichioka
Keyword(s):  
Differential Operator ◽  
Rank Order ◽  
Nonlinear Differential Operator

Existence of Multiple Solutions for Nonlinear Dirichlet Problems with a Nonhomogeneous Differential Operator

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Sophia Th. Kyritsi ◽  
Donal O’ Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Linear Differential Operator ◽  
Principal Eigenvalue ◽  
Critical Groups ◽  
Smooth Solutions ◽  
Dirichlet Problems ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Nonlinear Differential Operator ◽  
Linear Differential

AbstractWe consider nonlinear elliptic problems driven by a nonhomogeneous nonlinear differential operator. Using variational methods combined with Morse theory (critical groups), we prove two multiplicity results establishing three nontrivial smooth solutions. For the semilinear problem (linear differential operator), we produce four nontrivial smooth solutions. In the special case of the p-Laplacian differential operator, our framework of analysis incorporates equations which are resonant at infinity with respect to the principal eigenvalue.

A Metod with a Controllable Exponential Convergence Rate for Nonlinear Differential Operator Equations

2009 ◽  
Vol 9 (1) ◽  
pp. 63-78 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
I. I. Lazurchak ◽  
V. L. Makarov ◽  
D. Sytnyk
Keyword(s):  
Differential Operator ◽  
Convergence Rate ◽  
Nonlinear Operator ◽  
Control Mechanism ◽  
Exponential Convergence ◽  
Operator Equations ◽  
Exponential Convergence Rate ◽  
Convergence Control ◽  
Nonlinear Differential Operator ◽  
Theoretical Results

AbstractWe propose a new analytical-numerical method with an embedded convergence control mechanism for solving nonlinear operator differential equations. The method provides the exponential convergence rate. A numerical example confirms the theoretical results.

The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Miroslaw Lustyk ◽  
Julian Janus ◽  
Marzenna Pytel-Kudela ◽  
Anatoliy Prykarpatsky
Keyword(s):  
Differential Operator ◽  
Banach Spaces ◽  
Linear Differential Operator ◽  
Algebraic Approach ◽  
Discrete Approximations ◽  
Operator Equations ◽  
Solution Convergence ◽  
Nonlinear Differential Operator ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained.

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