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On Hammerstein equations with natural growth conditions. (English) Zbl 0942.45003
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.

MSC:
45G10 Other nonlinear integral equations
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiń≠, Uryson, etc.)
49J45 Methods involving semicontinuity and convergence; relaxation
49J52 Nonsmooth analysis
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