Geodesic
Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb{R})$
Archivum mathematicum, Tome 51 (2015) no. 2, pp. 87-105.

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We consider the equation \begin{equation} - r(x)y^{\prime }(x)+q(x)y(x)=f(x)\,,\quad x\in \mathbb{R} \end{equation} where $f\in L_p(\mathbb{R}) $, $p\in [1,\infty ]$ ($L_\infty (\mathbb{R}):=C(\mathbb{R})$) and \begin{equation} 0\in C^{}(\mathbb{R})\,,\quad 0\le q\in L_1^{}(\mathbb{R})\,. \end{equation} We obtain minimal requirements to the functions $r$ and $q$, in addition to (), under which equation () is correctly solvable in $L_p(\mathbb{R})$, $p\in [1,\infty ]$.
DOI : 10.5817/AM2015-2-87
Classification : 46E35
Keywords: correct solvability; differential equation of the first order 
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     title = {Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb{R})$},
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Chernyavskaya, N.; Shuster, L. A. Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb{R})$. Archivum mathematicum, Tome 51 (2015) no. 2, pp. 87-105. doi : 10.5817/AM2015-2-87. http://geodesic.mathdoc.fr/articles/10.5817/AM2015-2-87/

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