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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 3, 1999, pp. 625–638
DOI: 10.4171/ZAA/902

Published online: 1999-09-30

On Hammerstein Equations with Natural Growth Conditions

V. Moroz[1] and P. P. Zabrejko[2]

(1) The Academy of Sciences of Belarus, Minsk, Belarus
(2) The Academy of Sciences of Belarus, Minsk, Belarus

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

Moroz V., Zabrejko P. P.: On Hammerstein Equations with Natural Growth Conditions. Z. Anal. Anwend. 18 (1999), 625-638. doi: 10.4171/ZAA/902