Existence results in the \(\alpha \) -norm for a class of neutral partial functional Integro-differential equations

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• 作者：Boubacar Diao ; Khalil Ezzinbi ; Mamadou Sy
• 关键词：Integrodifferential equations ; Analytic semigroup ; Analytic resolvent operator fractional power of linear operators ; Neutral equation ; 35R09 ; 34K40 ; 47G20 ; 34K37
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：26
• 期：7-8
• 页码：1621-1635
• 全文大小：458 KB
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  5.Ezzinbi, K., Ghnimi, S., Taoudi, M.: Existence and regularity of solutions for neutral partial functional integrodifferential equations with infinite delay. Nonlinear Anal. 4, 54鈥?4 (2010)MATH MathSciNet
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  17.Travis, C.C., Webb, G.F.: Existence, stability and compactness in the \(\alpha \) -norm for partial functional differential equations. Trans. Am. Math. Soc. 240, 129鈥?43 (1978)MATH MathSciNet
  18.Adimy, M., Ezzinbi, K.: Existence and stability in the \(\alpha \) -norm for partial functional differential equations of neutral type. Ann. Mat. Pura Appl. Ser. IV 185(3), 437鈥?60 (2006)MATH MathSciNet CrossRef
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• 作者单位：Boubacar Diao (1)
  Khalil Ezzinbi (2)
  Mamadou Sy (1)
  
  1. Laboratoire L.A.N.I, Universit茅 Gaston Berger de Saint-Louis UFR SAT, BP 234, Saint-Louis, Senegal
  2. D茅partement de Math茅matiques, Facult茅 des Sciences Semlalia, Universit茅 Cadi Ayyad, BP 2390, Marrakesh, Morocco
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

The goal of this paper is to study, in the \(\alpha \)-norm the existence of solutions for a class of neutral partial functional integrodifferential equations with finite delay. We assume that the linear part generates an analytic and compact semigroup and the nonlinear part is continuous and involves spatial partial derivatives in the second argument. At the end an example is provided to illustrate the application of the obtained results. Keywords Integrodifferential equations Analytic semigroup Analytic resolvent operator fractional power of linear operators Neutral equation