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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Parabolicity of a class of higher order abstract differential equations
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by Ti Jun Xio and Jin Liang PDF
Proc. Amer. Math. Soc. 120 (1994), 173-181 Request permission

Abstract:

Let $E$ be a complex Banach space, ${c_i} \in \mathbb {C}\;(1 \leqslant i \leqslant n - 1)$, and $A$ be a nonnegative operator in $E$. We discuss the parabolicity of the higher-order abstract differential equations \begin{equation} \tag {$\ast $} {u^{(n)}}(t) + \sum \limits _{i = 1}^{n - 1} {{c_i}{A^{{k_i}}}{u^{(n - i)}}(t) + Au(t) = 0} \end{equation} and some perturbation cases of ($\ast$). A sufficient and necessary condition for ($\ast$) to be parabolic is obtained, provided ${k_1} > {k_2} - {k_1} > \cdots > 1 - {k_{n - 1}} > 0,\;{c_i} \ne 0\;(1 \leqslant i \leqslant n - 1)$. For $A$ strictly nonnegative (Definition 1.3), $n = 3,{c_1},{c_2} \geqslant 0$, a sharp criterion is given.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 120 (1994), 173-181
  • MSC: Primary 34G10; Secondary 47D09
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1182708-3
  • MathSciNet review: 1182708