Positive solutions of superlinear Hammerstein integral equations in Banach spaces (Q1127696)
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scientific article; zbMATH DE number 1185927
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive solutions of superlinear Hammerstein integral equations in Banach spaces |
scientific article; zbMATH DE number 1185927 |
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Positive solutions of superlinear Hammerstein integral equations in Banach spaces (English)
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28 March 1999
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The existence of one and two positive solutions of the Hammerstein equation in an ordered Banach space is considered. The essential assumptions on the nonlinear function are uniform continuity on balls, superlinearity with respect to the order, and a (mild) compactness assumption. The proofs make use of the fixed point index for condensing operators; a priori estimates are not required. Applications to the superlinear Sturm-Liouville equation in finite and infinite dimensions are given.
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superlinear Hammerstein integral equations
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positive solution
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ordered Banach space
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superlinear Sturm-Liouville equation
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