# SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS

Volume 2, Issue 3, pp 152-160
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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.

### Share and Cite

##### ISRP Style

A. M. A EL-SAYED, H. H. G HASHEM, SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS, Journal of Nonlinear Sciences and Applications, 2 (2009), no. 3, 152-160

##### AMA Style

EL-SAYED A. M. A, HASHEM H. H. G, SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS. J. Nonlinear Sci. Appl. (2009); 2(3):152-160

##### Chicago/Turabian Style

EL-SAYED, A. M. A, HASHEM, H. H. G. "SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS." Journal of Nonlinear Sciences and Applications, 2, no. 3 (2009): 152-160

### Keywords

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

•  39B82
•  44B20
•  46C05

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