tailieunhanh - báo cáo hóa học:" Research Article Nonlocal Impulsive Cauchy Problems for Evolution Equations"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Nonlocal Impulsive Cauchy Problems for Evolution Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 784161 17 pages doi 2011 784161 Research Article Nonlocal Impulsive Cauchy Problems for Evolution Equations Jin Liang1 and Zhenbin Fan1 2 1 Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China 2 Department of Mathematics Changshu Institute of Technology Suzhou Jiangsu 215500 China Correspondence should be addressed to Jin Liang jinliang@ Received 17 October 2010 Accepted 19 November 2010 Academic Editor Toka Diagana Copyright 2011 J. Liang and Z. Fan. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Of concern is the existence of solutions to nonlocal impulsive Cauchy problems for evolution equations. Combining the techniques of operator semigroups approximate solutions noncompact measures and the fixed point theory new existence theorems are obtained which generalize and improve some previous results since neither the Lipschitz continuity nor compactness assumption on the impulsive functions is required. An application to partial differential equations is also presented. 1. Introduction Impulsive equations arise from many different real processes and phenomena which appeared in physics chemical technology population dynamics biotechnology medicine and economics. They have in recent years been an object of investigations with increasing interest. For more information on this subject see for instance the papers cf. . 1-6 and references therein. On the other hand Cauchy problems with nonlocal conditions are appropriate models for describing a lot of natural phenomena which cannot be described using classical Cauchy problems. That is why in recent years they have been studied by many researchers cf. . 4 7-12 and references therein . In 4 the authors combined the two .

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