K. A. Khachatryan, T. E. Terdzhyan, “On the solvability of one class of nonlinear integral equations in <nobr>$L_1(0,+\infty)$</nobr>”, Mat. Tr., 2015, Volume 18, Number 1,Pages <nobr>190

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On the solvability of one class of nonlinear integral equations in $L_1(0,+\infty)$

K. A. Khachatryan^a, T. E. Terdzhyan^b

^a Institute of Mathematics of the NAS of Armenia, Yerevan, Armenia
^b Armenian National Agrarian University, Yerevan, Armenia

Abstract: We study the problem of constructing a solution that is positive, integrable, and essentially bounded on $(0,+\infty)$ to one class of nonlinear Hammerstein integral equations with noncompact operator in the critical case.

Key words: nonlinear equation, Hammerstein operator, space of integrable functions, convergence, monotonicity.

UDC: 517.968.74

Received: 11.11.2014

DOI: 10.17377/mattrudy.2015.18.107