Geodesic
Substitution method for generalized linear differential equations
Mathematica Bohemica, Tome 116 (1991) no. 4, pp. 337-359

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The generalized linear differential equation $dx=d[a(t)]x+df$ where $A,f\in BV^{loc}_n(J)$ and the matrices $I-\Delta^-\ A(t), I+\Delta^+\ A(t)$ are regular, can be transformed $\frac{dy}{ds}=B(s)y+g(s)$ using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.
The generalized linear differential equation $dx=d[a(t)]x+df$ where $A,f\in BV^{loc}_n(J)$ and the matrices $I-\Delta^-\ A(t), I+\Delta^+\ A(t)$ are regular, can be transformed $\frac{dy}{ds}=B(s)y+g(s)$ using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.
DOI : 10.21136/MB.1991.126028
Classification : 34A30, 34A99, 34D05, 34D99
Keywords: generalized linear differential equation; substitution method; variational stability; logarithmic prolongation; ordinary linear differential equation with a substitution 
Fraňková, Dana. Substitution method for generalized linear differential equations. Mathematica Bohemica, Tome 116 (1991) no. 4, pp. 337-359. doi: 10.21136/MB.1991.126028
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