On solvability of a class of nonlinear integral equations with Hammerstein type noncompact operator in the space $L_1(R^+)$

Kh. A. Khachatryan; T. H. Sardaryan

Geodesic

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On solvability of a class of nonlinear integral equations with Hammerstein type noncompact operator in the space $L_1(R^+)$

Kh. A. Khachatryan ; T. H. Sardaryan

Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2014), pp. 16-23

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Résumé

In the paper a class of nonlinear integral equations on the positive semi axis with noncompact Hammerstein type operator is studied. The existence of nontrivial, nonnegative, integrable and bounded on $R^+$ solution is proved. Some specific examples of these equations representing independent interest are given.

Keywords: Hammerstein type equation, one-parameter family of solutions, Caratheodory condition, iteration.
Mots-clés : monotony

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Kh. A. Khachatryan; T. H. Sardaryan. On solvability of a class of nonlinear integral equations with Hammerstein type noncompact operator in the space $L_1(R^+)$. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2014), pp. 16-23. http://geodesic.mathdoc.fr/item/UZERU_2014_3_a3/