On Hammerstein equations with natural growth conditions (Q1806184)
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scientific article; zbMATH DE number 1356399
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Hammerstein equations with natural growth conditions |
scientific article; zbMATH DE number 1356399 |
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On Hammerstein equations with natural growth conditions (English)
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20 December 1999
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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.
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natural growth conditions
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nonlinear Hammerstein integral equation
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energy functional
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non-smooth functionals
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direct variational method
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nontrivial solvability
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