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This article is cited in 5 scientific papers (total in 5 papers)
The solvability results for the third-order singular non-linear differential equation
Zh. B. Yeskabylovaa, K. N. Ospanova, T. N. Bekjanb a Department of Mechanics and Mathematics,
L.N. Gumilyov Eurasian National University,
13 Munaitpasov St.,
010008 Nur-Sultan, Kazakhstan
b Colledge of Mathematics and System Sciences,
Xinjiang University,
Urumqi, China
Abstract:
We give some conditions for solvability in $L_2(\mathbb{R})$ ($\mathbb{R}=(-\infty,+\infty)$) of the following
singular non-linear differential equation:
$$
ly\equiv-y'''(x)+q(x,y,y')y'+s(x,y,y')y=h(x).
$$
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
$$
||y'''||_2+||q(\cdot,y,y')y'||_2+||s(\cdot,y,y')y||_2<\infty,
$$
where $||\cdot||_2$ is the norm in $L_2$. To establish these facts, we use coercive solvability results for the
corresponding linear third-order differential equation obtained by us earlier.
Keywords and phrases:
non-linear differential equation, intermediate term, solvability, estimates of solutions.
Received: 17.08.2019
Citation:
Zh. B. Yeskabylova, K. N. Ospanov, T. N. Bekjan, “The solvability results for the third-order singular non-linear differential equation”, Eurasian Math. J., 10:4 (2019), 85–91
Linking options:
https://www.mathnet.ru/eng/emj350 https://www.mathnet.ru/eng/emj/v10/i4/p85
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