Geodesic
One parameter families of positive solutions of some classes of convolution type nonlinear integral equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 1, pp. 91-108

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We study a class of nonlinear integral equations of convolution type on the half line and on the whole line with noncompact Hammerstein operator. Under certain restrictions on the nonlinearity we prove the existence of one-parameter family of positive solutions and study the asymptotic behaviour of the solutions at infinity. To illustrate the results, we give some specific examples of the equations.
Keywords: monotonicity, iterations, one-parameter family of positive solutions, Caratheodory condition, set of parameters. 
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     author = {Kh. A. Khachatryan and H. S. Petrosyan},
     title = {One parameter families of positive solutions of some classes of convolution type nonlinear integral equations},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {91--108},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a7/}
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Kh. A. Khachatryan; H. S. Petrosyan. One parameter families of positive solutions of some classes of convolution type nonlinear integral equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 1, pp. 91-108. http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a7/