Function Space and Variational Problem for a Differential Equation with Degeneration
Oinarov R. Kalybay A.A.
December 2025Pleiades Publishing
Proceedings of the Steklov Institute of Mathematics
2025#331Issue 1148 - 164 pp.
Abstract: We introduce a function space on the positive real axis with multiweighted derivatives. A multiweighted derivative is defined as a successive differentiation procedure in which each derivative is taken after multiplying the function by a corresponding weight. The weight functions are assumed to be sufficiently smooth. We study the fundamental properties of this space and obtain weighted estimates for intermediate derivatives. Based on these results, we prove an existence and uniqueness theorem for generalized solutions of the Euler differential equation in this space for various types of degeneration on the boundary of the positive real axis. The solution is understood in the sense of the corresponding variational problem.
Euler equation , generalized solution , multiweighted derivative , quadratic form , space with multiweighted derivatives , variational equation , weight function
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L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
KIMEP University, Almaty, Kazakhstan
L. N. Gumilyov Eurasian National University
KIMEP University
10 лет помогаем публиковать статьи Международный издатель
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