Gronwall Inequality for Projected Systems
Key Words: differential equation   Gronwall inequality   bounded solution.  
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Zhang Weinian Centre for Math. Sci.
Academia Sinica Chengdu 610041 
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      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.
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