Solvability of a quadratic Hammerstein integral equation in the class of functions having limits at infinity. (English) Zbl 1223.45006
The authors prove that a quadratic Hammerstein integral equation has solutions in the class of real functions defined, bounded, continuous on the real half-axis and having limits at infinity. The main tool used in this investigation is the technique of measures of noncompactness and the Darbo fixed point theorem. At last, an example is performed.
Reviewer: Li Xing (Yinchuan)
MSC:
| 45G10 | Other nonlinear integral equations |
| 47H30 | Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) |
| 47H10 | Fixed-point theorems |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
Keywords:
quadratic Hammerstein integral equation; superposition operator; measure of noncompactness; Darbo fixed point theoremReferences:
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