Remarks on Projected Gronwall Inequality
Received:May 17, 1999  
Key Words: differential equation   Gronwall inequality   projection   hyperbolicity   discontinu-ity.  
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Author NameAffiliation
DENG Sheng-fu College of Mathematics
Sichuan University
Chengdu
China 
ZHANG Wei-nian College of Mathematics
Sichuan University
Chengdu
China 
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Abstract:
      Based on the discussion in [6] of projected Gronwall inequality u(t)≤ a(t)+∫0tb(t-s)u(s)ds+∫0c(s)u(t+s)ds,?t≥ 0,it is indicated that the condition that (?) a(t) = 0 in [6] is not necessary. Futhermore,with-out continuity of functions u(t), a(t), and c(t), and monotonicity of function a(t),a moregeneral result is obtained. This result can be properly used in the case of [5],and the newmethod of the proof can remedy the leak in [5].
Citation:
DOI:10.3770/j.issn:1000-341X.2002.02.025
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