On Hammerstein equations with natural growth conditions
Summary: We study a nonlinear Hammerstein integral equation by means of the direct variational method. Under certain ``natural'' growth conditions on the nonlinearity 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 nontrivial solvability results for the original equation are given.
scientific article; zbMATH DE number 1356399