A Characterization of Semilinear Dense Range Operators and Applications

H. Leiva, N. Merentes and J. Sanchez

Abstract and Applied Analysis, 2013, vol. 2013, 1-11

Abstract:

We characterize a broad class of semilinear dense range operators given by the following formula, , where , are Hilbert spaces, , and is a suitable nonlinear operator. First, we give a necessary and sufficient condition for the linear operator to have dense range. Second, under some condition on the nonlinear term , we prove the following statement: If , then and for all there exists a sequence given by , such that . Finally, we apply this result to prove the approximate controllability of the following semilinear evolution equation: , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous compact semigroup in , the control function belongs to , and is a suitable function. As a particular case we consider the controlled semilinear heat equation.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:729093

DOI: 10.1155/2013/729093

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