Open Access
24 December 2002 Bounded solutions of nonlinear Cauchy problems
Josef Kreulich
Abstr. Appl. Anal. 7(12): 637-661 (24 December 2002). DOI: 10.1155/S1085337502208015


For a given closed and translation invariant subspace Y of the bounded and uniformly continuous functions, we will give criteria for the existence of solutions uY to the equation u(t)+A(u(t))+ωu(t)f(t),t, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u(t)+A(u(t))+ωu(t)f(t),t>0,u(0)=u0, in general Banach spaces, where A denotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the space Y are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior.


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Josef Kreulich. "Bounded solutions of nonlinear Cauchy problems." Abstr. Appl. Anal. 7 (12) 637 - 661, 24 December 2002.


Published: 24 December 2002
First available in Project Euclid: 14 April 2003

zbMATH: 1048.47049
MathSciNet: MR1950613
Digital Object Identifier: 10.1155/S1085337502208015

Primary: 47H06 , 47J35
Secondary: 34C27

Rights: Copyright © 2002 Hindawi

Vol.7 • No. 12 • 24 December 2002
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