Some theorems on boundedness of solutions of ordinary differential equations

1961 ◽  
pp. 289-294 ◽  
Author(s):  
Yu. A. Klokov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundedness Of Solutions

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.

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