Advanced Search

We consider the equation $$-r\left(x\right)y^{\text{'}}\left(x\right)+q\left(x\right)y\left(x\right)=f\left(x\right),x\in ℝ$$ where $f\in L_p\left(ℝ\right)$, $p\in [1,\infty ]$ ($L_{\infty }\left(ℝ\right):=C\left(ℝ\right)$) and $$0<r\in C^{}\left(ℝ\right),0\le q\in L_1^{}\left(ℝ\right).$$ We obtain minimal requirements to the functions $r$ and $q$, in addition to (), under which equation () is correctly solvable in $L_p\left(ℝ\right)$, $p\in [1,\infty ]$.