scholarly journals On Stability of Linear Barbashin Type Integrodifferential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Michael Gil’
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Homogeneous Equation ◽  
Type Equation ◽  
Integrodifferential Equations ◽  
Stability Test ◽  
Boundedness Of Solutions ◽  
Operator Equations ◽  
Freezing Method ◽  
Solution Estimates

We consider the Barbashin type equation∂u(t,x)/∂t=c(t,x)u(t,x)+∫01k(t,x,s)u(t,s)ds+f(t,x)   (t>0; 0≤x≤1),wherec(·, ·),k(·, ·, ·), andf(·, ·)are given real functions andu(·, ·)is unknown. Conditions for the boundedness of solutions of this equation are suggested. In addition, a new stability test is established for the corresponding homogeneous equation. These results improve the well-known ones in the case when the coefficients are differentiable in time. Our approach is based on solution estimates for operator equations. It can be considered as the extension of the freezing method for ordinary differential equations.

A Problem-Solving Approach to the Introduction to Ordinary Differential Equations for Undergraduate Students at an American Two-year College

2019 ◽  
pp. 183-188
Author(s):  
John Gordon
Keyword(s):  
New York ◽  
Problem Solving ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Undergraduate Students ◽  
Homogeneous Equation ◽  
Introductory Course ◽  
Two Year College ◽  
Course Material ◽  
And Mathematics

Undergraduate students in STEM (Science, Technology, Engineering, and Mathematics) at City University of New York (CUNY)-Queensborough Community College (QCC) working toward a baccalaureate degree at one of CUNY’s senior colleges are required to take an introductory course in ordinary differential equations (ODE). Faculty in the Mathematics Department at QCC are experimenting with a problem-solving approach to this course in which students engage in learning course material through the development of mathematical models of real-world problems. The results seem promising and we outline them in this paper. Key-Words: First-order, linear system, integrating factor, homogeneous equation, research-based.

Singularly perturbed ordinary differential equations with dynamic limits

1996 ◽  
Vol 126 (3) ◽  
pp. 541-569 ◽  
Author(s):  
Zvi Artstein ◽  
Alexander Vigodner
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Invariant Measures ◽  
Type Equation ◽  
Slow Motion ◽  
Algebraic Equations ◽  
Direct Integral ◽  
Limit Behaviour ◽  
Unique Invariant Measure ◽  
Fast Flow

Coupled slow and fast motions generated by ordinary differential equations are examined. The qualitative limit behaviour of the trajectories as the small parameter tends to zero is sought after. Invariant measures of the parametrised fast flow are employed to describe the limit behaviour, rather than algebraic equations which are used in the standard reduced order approach. In the case of a unique invariant measure for each parameter, the limit of the slow motion is governed by a chattering type equation. Without the uniqueness, the limit of the slow motion solves a differential inclusion. The fast flow, in turn, converges in a statistical sense to the direct integral, respectively the set-valued direct integral, of the invariant measures.

A stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

2018 ◽  
Vol 11 (91) ◽  
pp. 4541-4548 ◽  
Author(s):  
Danilo Alonso Ortega Bejarano ◽  
Eduardo Ibarguen-Mondragon ◽  
Enith Amanda Gomez-Hernandez
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Stability Test ◽  
Non Linear ◽  
Non Linear Systems

Complementary variational principles for a class of differential equations

1972 ◽  
Vol 72 (2) ◽  
pp. 229-232 ◽  
Author(s):  
A. M. Arthurs ◽  
C. W. Coles
Keyword(s):  
Maximum Principle ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variational Principles ◽  
Minimum Principle ◽  
Operator Equations ◽  
The Maximum Principle ◽  
Multiple Operator

AbstractMaximum and minimum principles for certain ordinary differential equations of order 2m are derived in a unified manner from the theory of complementary variational principles for multiple operator equations. The minimum principle is known in the literature, but the maximum principle appears to be new.

Operator equation and related questions of stability of differential equations

2020 ◽  
Author(s):  
Lyubov' Orlik ◽  
Galina Zhukova
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Operator Equation ◽  
Electromagnetic Waves ◽  
Special Kind ◽  
Stability Criteria ◽  
Boundedness Of Solutions ◽  
Operator Equations ◽  
Electrical Systems ◽  
Volterra Operators

The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existence and uniqueness of such solutions. The spectral criteria for boundedness of solutions of operator equations and, as a consequence, sufficient spectral features boundedness of solutions of differential and differential-difference equations in Banach space. The results obtained for operator equations with operators and work of Volterra operators, allowed to extend to some systems of partial differential equations known spectral stability criteria for solutions of A. M. Lyapunov and also to generalize theorems on the exponential characteristic. The results of the monograph may be useful in the study of linear mechanical and electrical systems, in problems of diffraction of electromagnetic waves, theory of automatic control, etc. It is intended for researchers, graduate students functional analysis and its applications to operator and differential equations.

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