Nonlocal Cauchy problems for nonautonomous evolution equations

Jin Liang; James H. Liu; Ti-Jun Xiao

doi:10.3934/cpaa.2006.5.529

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2006, Volume 5, Issue 3: 529-535. Doi: 10.3934/cpaa.2006.5.529

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Nonlocal Cauchy problems for nonautonomous evolution equations

1.
Department of Mathematics, University of Science and Technology of China, Hefei 230026
2.
Department of Mathematics, James Madison University, Harrisonburg, VA 22807

Received: August 2005

Revised: March 2006

Published: September 2006

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Abstract

This paper is concerned with nonlocal Cauchy problems for semilinear nonautonomous evolution equations with compact evolution families on Banach spaces. A new existence result about mild solutions for the above problems is obtained without Lipschitz conditions on nonlinear and nonlocal terms.

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Mathematics Subject Classification: Primary: 34G20; Secondary: 35K90.

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