Communications in Mathematical Analysis

Positive Solutions for Abstract Hammerstein Equations and Applications

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

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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

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

First available in Project Euclid: 5 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Increasing operator fixed point index theory boundary value problems Hammerstein equation


Benmezai, A.; Graef, J. R.; Kong, L. Positive Solutions for Abstract Hammerstein Equations and Applications. Commun. Math. Anal. 16 (2014), no. 1, 47--65.

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