Communications in Mathematical Analysis
- Commun. Math. Anal.
- Volume 16, Number 1 (2014), 47-65.
Positive Solutions for Abstract Hammerstein Equations and Applications
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.
Commun. Math. Anal., Volume 16, Number 1 (2014), 47-65.
First available in Project Euclid: 5 January 2014
Permanent link to this document
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
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