SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS


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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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


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