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Keywords:
correct solvability; differential equation of the first order
correct solvability; differential equation of the first order
Summary:
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 $L_p(\mathbb{R})$, $p\in [1,\infty ]$.
References:
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