Geodesic
Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 89-100

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The paper studies a construction of nontrivial solution for a class of Hammerstein–Nemytskii type nonlinear integral equations on half-line with noncompact Hammerstein integral operator, which belongs to space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$. This class of equations is the natural generalization of Wiener-Hopf type conservative integral equations. Examples are given to illustrate the results. For one type of considering equations continuity and uniqueness of the solution is established.
Classification : 45G05, 47H30
Keywords: Wiener–Hopf operator; Hammerstein–Nemytskii equation; Caratheodory condition; one-parameter family of positive solutions; iteration; monotonic increasing and bounded solution 
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     title = {Hammerstein{\textendash}Nemytskii {Type} {Nonlinear} {Integral} {Equations} on {Half-line} in {Space} $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Khachatryan, Aghavard Kh.; Khachatryan, Khachatur A. Hammerstein–Nemytskii Type Nonlinear Integral Equations on Half-line in Space $L_1(0,+\infty )\cap L_{\infty }(0,+\infty )$. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 1, pp. 89-100. http://geodesic.mathdoc.fr/item/AUPO_2013__52_1_a7/