The solvability conditions for the second order nonlinear differential equation with unbounded coefficients in L2(R)
L2(R)-де шенелмеген коэффициенттерi бар екiншi реттi сызықтықемес дифференциалдық теңдеудiң шешiлу шарттары
Условия разрешимости нелинейного дифференциального уравнения второго порядка с неограниченными коэффициентами в L2(R)
Yesbayev A.N. Ospanov M.N.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#101Issue 1104 - 110 pp.
The article deals with the existence of a generalized solution for the second order nonlinear differential equation in an unbounded domain. Intermediate and lower coefficients of the equation depends on the required function and considered smooth. The novelty of the work is that we prove the solvability of a nonlinear singular equation with the leading coefficient not separated from zero. In contrast to the works considered earlier, the leading coefficient of the equation can tend to zero, while the intermediate coefficient tends to infinity and does not depend on the growth of the lower coefficient. The result obtained formulated in terms of the coefficients of the equation themselves; there are no conditions on any derivatives of these coefficients.
differential equation in an unbounded domain , generalized solution , nonlinear differential equation , second order differential equation , solvability
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L.N.Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
L.N.Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
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