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Positive solutions for a Hammerstein integral equation with a parameter

✍ Scribed by Xi-Lan Liu; Jian-Hua Wu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
352 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

We discuss the existence of positive solutions for the Hammerstein integral equation

By calculation of the fixed point index in a cone, we obtain that there exists a critical value λ * > 0 such that the above equation has at least two, one positive solutions for λ ∈ (0, λ * ), λ = λ * , respectively, and has no positive solution for λ > λ * .

πŸ“œ SIMILAR VOLUMES

On solutions of a quadratic integral equ
On solutions of a quadratic integral equation of Hammerstein type
✍ J. BanaΕ›; J. Rocha Martin; K. Sadarangani πŸ“‚ Article πŸ“… 2006 πŸ› Elsevier Science 🌐 English βš– 211 KB

We study the solvability of a nonlinear quadratic integral equation of Hammerstein type. Using the technique of measures of noncompactness we prove that this equation has solutions on an unbounded interval. Moreover, we also obtain an asymptotic characterization of these solutions. Several special c