On Hammerstein Equations with Natural Growth Conditions
V. MorozThe Academy of Sciences of Belarus, Minsk, Belarus
P. P. ZabrejkoThe 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.
Cite this article
V. Moroz, P. P. Zabrejko, On Hammerstein Equations with Natural Growth Conditions. Z. Anal. Anwend. 18 (1999), no. 3, pp. 625–638DOI 10.4171/ZAA/902