Bounded Solutions for some Gradient Type Systems

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Bounded Solutions for some Gradient Type Systems

Show simple item record Aftabizadeh, A. R. en 2010-06-11T17:24:44Z en 2010-06-11T17:24:44Z en 1981-04 en
dc.identifier.uri en
dc.description.abstract C. Corduneanu in [3,TH.1] investigated the existence of a unique bounded solution of the system [see pdf for notation] (1.1) with [see pdf for notation] continuous and of class c(2) in u. In this paper we shall prove the existence of a unique bounded solution of (1.1), stated in [3,TR.1], under weaker conditions, and also we shall discuss the asymptotic behavior of bounded solution of (1.1) on a half-line. We wish to mention that M. M. Belova [1] had similar ideas, but she did consider only a special case (space L2), and without concern for existence. Before we proceed further, we present some results, without proofs, which help simplify the proofs of our main results. Lemma 1.1 is analogous to Lemma 2 of [2, P. 102], Theorem 1.1 is analogous to Theorem 1 of [3], and Lemma 1.2 is a special case of Theorem 1.1. We also need the following definitions for M and M0. [see pdf for notation] where the norm in M0 is the same as in M, also it is easy to see that M0 C M. The author is grateful to professor C. Corduneanu for all his suggestions and comments made during the preparation of this paper. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;158 en
dc.subject Unique bounded solution en
dc.subject Asymptotic properties en
dc.subject.lcsh Mathematics Research en
dc.title Bounded Solutions for some Gradient Type Systems en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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