SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS

Volume 2, Issue 3, pp 152-160 http://dx.doi.org/10.22436/jnsa.002.03.02

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Authors

A. M. A EL-SAYED - Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt.. H. H. G HASHEM - Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt..

Abstract

We are concerning with a nonlinear Hammerstein quadratic integral equation. We prove the existence of at least one positive solution \(x \in L_1\) under Carathµeodory condition. Secondly we will make a link between Peano condition and Carathµeodory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved.

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Keywords

• Hammerstein quadratic integral equation
• Continuous solutions
• Positive integrable solutions
• Maximal and minimal solutions.

MSC

•  39B82
•  44B20
•  46C05

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