Optimal control of a functional equation

associated with closed range

selfadjoint operators

Authors:
S. C. Gao and N. H. Pavel

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2979-2986

MSC (1991):
Primary 47N10, 47B25, 49K27.

DOI:
https://doi.org/10.1090/S0002-9939-98-04633-4

MathSciNet review:
1473668

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Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions for the optimality of a pair subject to are given. Here is a selfadjoint operator with closed range on a Hilbert space and . The case - unbounded is also discussed, which leads to some open problems. This general functional scheme includes most of the previous results on the optimal control of the -periodic wave equation for all in a dense subset of . It also includes optimal control problems for some elliptic equations.

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Additional Information

**S. C. Gao**

Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701

Email:
shugao@bing.math.ohiou.edu

**N. H. Pavel**

Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701

Email:
npavel@bing.math.ohiou.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04633-4

Keywords:
Self-adjoint operators with closed range,
optimal pairs,
maximum principles,
periodic waves

Additional Notes:
The research of the first author was supported in part by the National Science Foundation of China

The research of the second author was supported in part by the National Research Fund, Korean Research Foundation Project #01-D0406 (jointly with Prof. J. K. Kim)

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society