Gronwall Inequality for Projected Systems
  
Key Words: differential equation   Gronwall inequality   bounded solution.  
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Author NameAffiliation
Zhang Weinian Centre for Math. Sci.
CICA
Academia Sinica Chengdu 610041 
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Abstract:
      In this paper we discuss a problem about Gronwall inequality for projected systems, which was mentioned in Hale′s book. An estimate for nonnegative bounded continuous function u(t)≤a(t)+∫tb(t-s)u(s)ds+∫c(s)u(t+s)ds,(?)t≥0 is given. The conclusion is useful for investigating bounded solutions, invariant manifolds and its foliations for differential equations, and for further discussion on Gronwall inequality with singularity.
Citation:
DOI:10.3770/j.issn:1000-341X.1997.02.023
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