Differential inequality and non-oscillation of fourth order differential equation
Дифференциалдық теңсiздiк және төртiншi реттi дифференциалдық теңдеудiң тербелiмсiздiгi
Дифференциальное неравенство и неосцилляторность дифференциального уравнения четвертого порядка
Kalybay A.A. Baiarystanov A.O.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#104Issue 4103 - 109 pp.
The oscillatory theory of fourth order differential equations has not yet been developed well enough. The results are known only for the case when the coefficients of differential equations are power functions. This fact can be explained by the absence of simple effective methods for studying such higher order equations. In this paper, the authors investigate the oscillatory properties of a class of fourth order differential equations by the variational method. The presented variational method allows to consider any arbitrary functions as coefficients, and our main results depend on their boundary behavior in neighborhoods of zero and infinity. Moreover, this variational method is based on the validity of a certain weighted differential inequality of Hardy type, which is of independent interest. The authors of the article also find two-sided estimates of the least constant for this inequality, which are especially important for their applications to the main results on the oscillatory properties of these differential equations.
fourth order differential equation , non-oscillation , oscillation , space , variational principle , weighted inequality
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KIMEP University, Almaty, Kazakhstan
L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
KIMEP University
L.N. Gumilyov Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026