On retarded integral inequalities and their applications

By Yuangong Sun. 2005

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Abstract The main results of [J. Math. Anal. Appl. 285 (2003) 436–443] are here generalized to the following retarded integral inequalities: u m ( t ) ⩽ c m / ( m − n ) + m m − n ∫ 0 α ( t ) [ f ( s ) u n ( s ) w ( u ( s ) ) + g ( s ) u n ( s ) ] d s and u m ( t ) ⩽ c m / ( m − n ) + m m − n ∫ 0 α ( t ) f ( s ) u n ( s ) w ( u ( s ) ) d s + m m − n ∫ 0 t g ( s ) u n ( s ) w ( u ( s ) ) d s , where m > n > 0 are constants and t ∈ R + = [ 0 , ∞ ) . The results given here can be applied to the global existence of solutions to differential equations with time delay.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82df1d2208769947fb3f8a389211dc0322492224