Analog of Hayman's Theorem and its Application to Some System of Linear Partial Differential Equations
DOI:
https://doi.org/10.15407/mag15.02.170Анотація
Аналог відомої теореми Хеймана застосовується до дослідження обмеженості $\mathbf{L}$-індексу за сукупністю змінних цілих розв'язків деяких лінійних систем рівнянь з частинними похідними вищих порядків та знайдено достатні умови, які гарантують цю обмеженість, де $\mathbf{L}(z)=(l_1(z),\ldots,l_{n}(z)),$ $l_j:\mathbb{C}^n\to \mathbb{R}_+$~--- неперервна функція, $j\in\{1,\ldots,n\}.$ Також отримано оцінки зростання цих розв'язків. Наведено приклади систем РЧП, які доводять точність встановлених оцінок для цілих розв'язків. Отримані результати також є новими в одновимірному випадку, бо послаблено додаткові умови на додатну неперервну функцію $l.$
Mathematics Subject Classification: 32W50, 32A15, 32A22, 35G35, 32A40.
Ключові слова:
ціла функція, обмежений $\mathbf{L}$-індекс за сукупністю змінних, лінійна система РЧП вищих порядків, аналітична теорія РЧП, цілий розв'язок, лінійне диференціальне рівняння вищого порядкуПосилання
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