Parabolicity of a class of higher order abstract differential equations

Authors:
Ti Jun Xio and Jin Liang

Journal:
Proc. Amer. Math. Soc. **120** (1994), 173-181

MSC:
Primary 34G10; Secondary 47D09

MathSciNet review:
1182708

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Abstract: Let be a complex Banach space, , and be a nonnegative operator in . We discuss the parabolicity of the higher-order abstract differential equations

() |

and some perturbation cases of (). A sufficient and necessary condition for () to be parabolic is obtained, provided . For strictly nonnegative (Definition 1.3), , a sharp criterion is given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1182708-3

Keywords:
Parabolicity,
higher-order abstract differential equation,
nonnegative operator,
strictly nonnegative,
perturbation

Article copyright:
© Copyright 1994
American Mathematical Society