EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 3, pp. 625-638 (1999)

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On Hammerstein Equations with Natural Growth Conditions

V. Moroz and P. Zabreiko

Both authors: State Univ., Mech.-Math. Dept., Skariny Av. 4, 220080 Minsk, Belarus; moroz@mmf.bsu.unibel.by \ \ and \ \ zabreiko@mmf.bsu.unibel.by

Abstract: In this paper we study a nonlinear Hammerstein integral equation by means of the direct variational method. Under certain natural growth conditions on the non-linearity we show that the existence of a local minimum for the energy functional implies the solvability of the original equation. In these settings the energy functional may be non-smooth on its domain and, moreover, operators in data may be non-compact. Some solvability and non-trivial solvability results for the original equation are given.

Keywords: hammerstein equations, direct variational method, non-smooth functionals

Classification (MSC2000): 45G10, 47H30, 49J45, 49J52

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Electronic fulltext finalized on: 7 Aug 2001. This page was last modified: 9 Nov 2001.

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