scholarly journals Boundedness and asymptotic stability in the large of solutions of an ordinary differential system y' = f(t, y, y')

1992 ◽  
Vol 5 (3) ◽  
pp. 261-274
Author(s):  
M. Venkatesulu ◽  
P. D. N. Srinivasu
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Differential System ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Stability Of Solutions ◽  
Initial Value ◽  
First Order ◽  
Ordinary Differential System ◽  
Physical Phenomena

Differential equations of the form y′=f(t,y,y′), where f is not necessarily linear in its arguments, represent certain physical phenomena and solutions have been known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier existence of solutions of first order initial value problems and stability of solutions of first order ordinary differential system of the above type were established. In this paper we study boundedness and asymptotic stability in the large of solutions of an ordinary differential system of the above type under certain natural hypotheses on f.

scholarly journals Stability of solutions of a nonstandard ordinary differential system by Lyapunov's second method

1991 ◽  
Vol 4 (3) ◽  
pp. 211-224
Author(s):  
M. Venkatesulu ◽  
P. D. N. Srinivasu
Keyword(s):  
Unique Solution ◽  
Differential System ◽  
Initial Value Problem ◽  
Stability Of Solutions ◽  
Initial Value ◽  
First Order ◽  
Ordinary Differential System ◽  
Lyapunov’S Second Method ◽  
The Stability ◽  
Physical Phenomena

Differential equations of the form y′=f(t,y,y′) where f is not necessarily linear in its arguments represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier we established the existence of a (unique) solution of the nonstandard initial value problem y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper, we studied the stability of solutions of a nonstandard first order ordinary differential system.

scholarly journals Numerical solutions of nonstandard first order initial value problems

1992 ◽  
Vol 5 (1) ◽  
pp. 69-82 ◽  
Author(s):  
M. Venkatesulu ◽  
P. D. N. Srinivasu
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Unique Solution ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Initial Value ◽  
First Order ◽  
Physical Phenomena

Differential equations of the form y′=f(t,y,y′), where f is not necessarily linear in its arguments, represent certain physical phenomena and are known for quite some time. The well known Clairut's and Chrystal's equations fall into this category. Earlier, we established the existence of a (unique) solution of the nonstandard initial value problem (NSTD IV P) y′=f(t,y,y′), y(t0)=y0 under certain natural hypotheses on f. In this paper we present some first order convergent numerical methods for finding the approximate solutions of the NST D I V Ps.

scholarly journals Initial value problems for integro-differential equations of Volterra type in Banach spaces

1994 ◽  
Vol 7 (1) ◽  
pp. 13-23 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Extremal Solutions ◽  
Comparison Result ◽  
Initial Value ◽  
Volterra Type ◽  
First Order

This paper investigates the extremal solutions of initial value problems for first order integro-differential equations of Volterra type in Banach spaces by means of establishing a comparison result.

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