Correct solvability of a general differential equation of the first order in the space $L_p\left(ℝ\right)$

Chernyavskaya, N., and Shuster, L.A.. "Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb {R})$." Archivum Mathematicum 051.2 (2015): 87-105. <http://eudml.org/doc/270119>.

@article{Chernyavskaya2015,
abstract = {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<r\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 $L_p(\mathbb \{R\})$, $p\in [1,\infty ]$.},
author = {Chernyavskaya, N., Shuster, L.A.},
journal = {Archivum Mathematicum},
keywords = {correct solvability; differential equation of the first order},
language = {eng},
number = {2},
pages = {87-105},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb \{R\})$},
url = {http://eudml.org/doc/270119},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Chernyavskaya, N.
AU - Shuster, L.A.
TI - Correct solvability of a general differential equation of the first order in the space $L_p(\mathbb {R})$
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 2
SP - 87
EP - 105
AB - 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<r\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 $L_p(\mathbb {R})$, $p\in [1,\infty ]$.
LA - eng
KW - correct solvability; differential equation of the first order
UR - http://eudml.org/doc/270119
ER -