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September  2006, 5(3): 529-535. doi: 10.3934/cpaa.2006.5.529

Nonlocal Cauchy problems for nonautonomous evolution equations

Jin Liang 1, , James H. Liu 2, and  Ti-Jun Xiao 1,

1. 

Department of Mathematics, University of Science and Technology of China, Hefei 230026
2. 

Department of Mathematics, James Madison University, Harrisonburg, VA 22807, United States

Received  August 2005 Revised  March 2006 Published  June 2006

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.
Keywords: Nonlocal Cauchy problem, compact evolution family, mild solution., nonautonomous evolution equation.
Mathematics Subject Classification: Primary: 34G20; Secondary: 35K9.
Citation: Jin Liang, James H. Liu, Ti-Jun Xiao. Nonlocal Cauchy problems for nonautonomous evolution equations. Communications on Pure and Applied Analysis, 2006, 5 (3) : 529-535. doi: 10.3934/cpaa.2006.5.529
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