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JOURNALS // Siberian Journal of Pure and Applied Mathematics // Archive

Sib. J. Pure and Appl. Math., 2017 Volume 17, Issue 1, Pages 91–108 (Mi vngu433)

This article is cited in 4 papers

One parameter families of positive solutions of some classes of convolution type nonlinear integral equations

Kh. A. Khachatryana, H. S. Petrosyanb

a Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan
b National Agrarian University of Armenia

Abstract: 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.

UDC: 517.968.4

Received: 17.09.2015

DOI: 10.17377/PAM.2017.17.108


 English version:
Journal of Mathematical Sciences, 2018, 231:2, 153–167


© Steklov Math. Inst. of RAS, 2025