Analytic linearization and complex powers of a nonlinear differential operator

1980 ◽  
Vol 14 (3) ◽  
pp. 213-214
Author(s):  
A. V. Babin
Keyword(s):  
Differential Operator ◽  
Nonlinear Differential Operator ◽  
Complex Powers

scholarly journals Complex powers of a differential operator related to the Schrodinger operator

2017 ◽  
Author(s):  
А.В. Гиль ◽  
В.А. Ногин
Keyword(s):  
Differential Operator ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Complex Powers

Изучаются комплексные степени дифференциального оператора второго порядка $S_{\overline{\lambda}}$, с комплексными коэффициентами в главной части. Отрицательные степени этого оператора реализованы как потенциалы $H_{\overline{\lambda}}^{\alpha}\varphi$ с нестандартной метрикой. Положительные степени, обратные к отрицательным,~--- как аппроксимативные обратные операторы. Описан также образ $H_{\overline{\lambda}}^{\alpha}(L_p)$ в терминах оператора, левого обратного к $H_{\overline{\lambda}}^{\alpha}$.

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.

Complex powers of a nonelliptic differential operator in L p -spaces

2013 ◽  
Vol 49 (10) ◽  
pp. 1282-1289
Author(s):  
D. N. Karasev ◽  
V. A. Nogin
Keyword(s):  
Differential Operator ◽  
Complex Powers

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.

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