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.
Citation:
Kh. A. Khachatryan, H. S. Petrosyan, “One parameter families of positive solutions of some classes of convolution type nonlinear integral equations”, Sib. J. Pure and Appl. Math., 17:1 (2017), 91–108; J. Math. Sci., 231:2 (2018), 153–167
\Bibitem{KhaPet17}
\by Kh.~A.~Khachatryan, H.~S.~Petrosyan
\paper One parameter families of positive solutions of some classes of convolution type nonlinear integral equations
\jour Sib. J. Pure and Appl. Math.
\yr 2017
\vol 17
\issue 1
\pages 91--108
\mathnet{http://mi.mathnet.ru/vngu433}
\crossref{https://doi.org/10.17377/PAM.2017.17.108}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 231
\issue 2
\pages 153--167
\crossref{https://doi.org/10.1007/s10958-018-3812-2}
Linking options:
https://www.mathnet.ru/eng/vngu433
https://www.mathnet.ru/eng/vngu/v17/i1/p91
This publication is cited in the following 4 articles:
Kh. A. Khachatryan, H. S. Petrosyan, “An iterative method for solving one class of non-linear integral equations
with Nemytskii operator on the positive semi-axis”, Izv. Math., 88:4 (2024), 760–793
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022) (to appear)
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 446–479
Kh. A. Khachatryan, A. K. Kroyan, “The existence of odd solution for one boundary-value problem with power nonlinearity”, J. Math. Sci., 253:3 (2021), 382–390
Citation in format AMSBIB
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