The Bojanov – Naidenov problem for functions with nonsymmetric restrictions on the highest derivative

• Date: 2019
• Main Authors: Kofanov, V. A., Кофанов, В. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1445
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For given $r \in \bfN , p, \alpha , \beta , \mu > 0$, we solve the extreme problems $$\int^b_ax^q_{\pm} (t)dt \rightarrow \mathrm{s}\mathrm{u}\mathrm{p}, q \geq p,$$ in the set of pairs $(x, I)$ of functions $x \in L^r_{\infty}$ and intervals $I = [a, b] \subset R$ satisfying the inequ...