Communications in Mathematical Analysis

Positive Solutions for Abstract Hammerstein Equations and Applications

A. Benmezai, J. R. Graef, and L. Kong

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Abstract

The authors use fixed point index properties to prove existence of positive solutions to the abstract Hammerstein equation $u=LFu$ where $L:E\rightarrow E$ is a compact linear operator, $F:K\rightarrow K$ is a continuous and bounded mapping, $E$ is a Banach space, and $K$ is a cone in $E$. The results obtained are used to prove existence results for positive solutions to two point boundary value problems associated with differential equations.

Article information

Source
Commun. Math. Anal., Volume 16, Number 1 (2014), 47-65.

Dates
First available in Project Euclid: 5 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1388953733

Mathematical Reviews number (MathSciNet)
MR3161735

Zentralblatt MATH identifier
1296.47056

Subjects
Primary: 47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces 37C25: Fixed points, periodic points, fixed-point index theory 34B15: Nonlinear boundary value problems

Keywords
Increasing operator fixed point index theory boundary value problems Hammerstein equation

Citation

Benmezai, A.; Graef, J. R.; Kong, L. Positive Solutions for Abstract Hammerstein Equations and Applications. Commun. Math. Anal. 16 (2014), no. 1, 47--65. https://projecteuclid.org/euclid.cma/1388953733


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