Geodesic
SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS
EL-SAYED, A. M. A 1 ; HASHEM, H. H. G 1
1 Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt.
Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 3, p. 152-160.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.002.03.02
Classification : 39B82, 44B20, 46C05
Keywords: Hammerstein quadratic integral equation, Continuous solutions, Positive integrable solutions, Maximal and minimal solutions.

EL-SAYED, A. M. A  1 ; HASHEM, H. H. G  1

1 Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt. 
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EL-SAYED, A. M. A ; HASHEM, H. H. G . SOLVABILITY OF NONLINEAR HAMMERSTEIN QUADRATIC INTEGRAL EQUATIONS. Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 3, p. 152-160. doi : 10.22436/jnsa.002.03.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.002.03.02/

[1] Banas, J.; Goebel, K. Measure of noncompactness in Banach space, Lecture Note in Pure and Appl. Math. , vol. 60. Dekker, New York, 1980

[2] Banas, J.; Lecko, M.; El-Sayed, W. G. Eixstence theorems of some quadratic integral equation, J.Math. Anal. Appl., Volume 227 (1998), pp. 276-279

[3] Banas, J.; A. Martinon Monotonic solutions of a quadratic integral equation of Volterra type, Comput. Math. Appl., 271 -279, 2004

[4] Banas, J.; Rzepka, B. Monotonic solutions of a quadratic integral equations of fractional order, J. Math. Anal. Appl. , Volume 332 (2007), pp. 1370-11378

[5] Emmanuele, G. Integrable solution of Hamnmerstien integral equation, Applicable Analysis Vol. 50 , 277-284, 1993

[6] Curtain, R. F.; A. J. Pritchard Functional Analysis in Modern Applied Mathematics Academic press, , , 1977

[7] Deimling, K. Nonlinear Functional Analysis, Springer - Verlag, Berlin, 1985

[8] EL-Sayed, A. M. A.; Hashem, H. H. G. Carathéodory type theorem for a nonlinear quadratic integral equation, MATH. SCI. RES. J. , Volume 12(4) (2008), pp. 71-95

[9] EL-Sayed, A. M. A.; Hashem, H. H. G. Integrable and continuous solutions of nonlinear quadratic integral equation, Electronic Journal of Qualitative Theory of Differential Equations, Volume 25 (2008), pp. 1-10

[10] EL-Sayed, A. M. A.; Hashem, H. H. G. Monotonic positive solution of nonlinear quadratic Hammerstein and Urysohn functional integral equations, Commentationes Mathematicae, Volume 48 (2008), pp. 199-207

[11] EL-Sayed, A. M. A.; Hashem, H. H. G. Weak maximal and minimal solutions for Hammerstein and Urysohn integral equations in reflexive Banach spaces, Differential Equation and Control Processes, Volume 4 (2008), pp. 50-62

[12] EL-Sayed, A. M. A.; Hashem, H. H. G. Monotonic solutions of functional integral and differential equations of fractional order, E. J. Qualitative Theory of Diff. Equ., Volume 7 (2009), pp. 1-8

[13] Lakshmikantham, V.; Leela, S. Differential and Integral Inequalities, Vol. 1, NewYork- London, 1969

[14] G. Scorza Dragoni Un teorema sulle funzioni continue rispetto ad una e misurabili rispetto ad un altra variabile, Rend. Sem. Mat. Univ. Padova , Volume 17 (1948), pp. 102-106

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