The solvability results for the third-order singular non-linear differential equation - Ospanov, Kordan; Yeskabyolva, Zhuldyz; Bekjan, Turdebek Nurlybekuly (Eurasian Mathematical Journal, 2019)
We give some conditions for solvability in L2(ℝ) (ℝ = (-∞, +∞)) of the following singular non-linear differential equation: ly ≡ -y″″″(x) + q(x, y, y′) y′ + s(x, y, y′) y = h(x). We assume that q and s are real-valued unbounded functions and q does not obey the “potential” s. For the solution y we prove that ‘‘y″″″’’2 + ‘‘q(∙, y, y′) y′’’2 + ‘‘s(∙, y, y′) y’’2 < ∞, where ‘‘·’’2 is the norm in L2. To establish these facts, we use coercive solvability results for the corresponding linear third-order differential equation obtained by us earlier.