scholarly journals Two parameter families of binary differential equations

2008 ◽  
Vol 22 (3) ◽  
pp. 759-789 ◽  
Author(s):  
Farid Tari ◽  
Keyword(s):  
Differential Equations ◽  
Binary Differential Equations ◽  
Two Parameter

An eigenfunction expansion associated with a two-parameter system of differential equations. III

1983 ◽  
Vol 93 (3-4) ◽  
pp. 189-195 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Differential Equations ◽  
Uniform Convergence ◽  
Ordinary Differential Equations ◽  
Eigenfunction Expansion ◽  
Second Order ◽  
System Of Differential Equations ◽  
Parameter System ◽  
Two Parameter

SynopsisWe continue with the work of earlier papers concerning the use of partial dilferential equations to prove the uniform convergence of the eigenfunction expansion associated witha left definite two-parameter system of ordinary differential equations of the second order.

LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX-1

2012 ◽  
Vol 12 (04) ◽  
pp. 1250002 ◽  
Author(s):  
NGUYEN DINH CONG ◽  
NGUYEN THI THE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lyapunov Exponents ◽  
Algebraic Equation ◽  
Differential Algebraic Equations ◽  
Lyapunov Spectrum ◽  
Stochastic Flow ◽  
Algebraic Equations ◽  
Differential Algebraic Equation ◽  
Two Parameter

We introduce a concept of Lyapunov exponents and Lyapunov spectrum of a stochastic differential algebraic equation (SDAE) of index-1. The Lyapunov exponents are defined samplewise via the induced two-parameter stochastic flow generated by inherent regular stochastic differential equations. We prove that Lyapunov exponents are nonrandom.

scholarly journals The first integrals and rational solutions of some fourth-order differential equations

2020 ◽  
Vol 56 (3) ◽  
pp. 318-327
Author(s):  
E. R. Babich ◽  
I. P. Martynov
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Rational Solution ◽  
Resonance Method ◽  
First Integrals ◽  
Rational Solutions ◽  
Analytical Properties ◽  
Special Points ◽  
Two Parameter

The object of this research is fourth-order differential equations. The aim of the research is to study the analytical properties of the solutions of these differential equations. The general form of the considered equations is indicated, and also the choice of the research object is justified. Herein we studied fourth-order differential equations for which sets of resonances with all positive nontrivial resonances are absent. Besides, three of these equations satisfy the conditions of absence in the solutions of moving multivalued singular points. The solutions of the next three equations have movable special points of multivalued character. Moreover, we also investigated the analytical properties of one more fourth-order differential equation of another general form for which it is also possible to construct a two-parameter rational solution as there is a nontrivial negative resonance in the related set of resonances. The first integrals of the equations under study are found and their rational solutions are constructed from negative non-trivial resonances. The resonance method was used in this study. The obtained results can be used in the analytical theory of differential equations.

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