Geodesic
Rezolventa Linearne Diferencijalne Jednačine
Nastava matematike, LIV (2009) no. 4, p. 20 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $\dot{x}=A(t)x$ be a homogeneous linear differential equation, where $A(t)$ is a continuous operator-valued function defined on an interval $T$, taking values in the space $L(R^{n};R^{n})$. The resolvent of this equation is the operator-valued function $R(t,\tau)$, defined on the square $T\times T$, satisfying conditions $ R_{t}(t,au)=A(t)\circ R(t,au),\quad R(au,au)=I, $ where $I\in L(R^{n};R^{n})$ is the identity operator. A connection between the resolvent and the Cauchy function is deduced. In particular, the resolvent is used for finding partial derivatives of the Cauchy function.
Classification : 1AMS97I70 2ZDMI75
Keywords: Differential equation, Reslovent, Cauchy function. 
@article{NM_2009_LIV_4_a4,
     author = {Vladimir Jankovi\'c},
     title = {Rezolventa {Linearne} {Diferencijalne} {Jedna\v{c}ine}},
     journal = {Nastava matematike},
     pages = {20 },
     year = {2009},
     volume = {LIV},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NM_2009_LIV_4_a4/}
}
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Vladimir Janković. Rezolventa Linearne Diferencijalne Jednačine. Nastava matematike, LIV (2009) no. 4, p. 20 . http://geodesic.mathdoc.fr/item/NM_2009_LIV_4_a4/