## Communications in Mathematical Analysis

### Positive Solutions for Abstract Hammerstein Equations and Applications

#### 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

#### 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