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A Leray-Schauder type theorem and applications to boundary value problems for neutral equations

Sengadir, T and Pai, DV and Pani, AK (1997) A Leray-Schauder type theorem and applications to boundary value problems for neutral equations. In: Nonlinear Analysis, 28 (4). pp. 701-719.

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Abstract

Consider the following two theorems which motivate the main result of this paper. THEOREM 1.1 (Fitzpatrick and Petryshyn [l]). Let X be a Frechet space and let D be an open neighbourhood of 0. Suppose that F : o- X is a continuous x-condensing map such that (a) hx # F(x), x E W and h > 1. Then F has a fixed point. Here, for a subset D of X, i3D and D denote the boundary and closure of D, respectively. Further, x is the ball measure of noncompactness on X defined as in [2].

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Measure of noncompactness;Frechet Spaces;fixed point theorems;neutral functional differential equations.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 31 Aug 2009 08:36
Last Modified: 19 Sep 2010 05:00
URI: http://eprints.iisc.ernet.in/id/eprint/18267

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