\documentclass[a4paper,11pt,numreferences,mathsec,kaplist]{isueps} \usepackage{isu} \begin{document} \setcounter{aqwe}{2} \begin{article} \begin{opening} \udk{518.517} \msc{123} \title{Multilinear integral \\ Volterra equation of the first kind:\\ elements of the theory and numerical methods\thanks {This work was supported by RFBR grant 00 - 00 -00000.}} \author{I. I.~\surname{Ivanov}} \institute{Irkutsk State University, Irkutsk, Russian Federation} \author{P. P.~\surname{Petrov}} \institute{Novosibirsk State University, Novosibirsk, Russian Federation} \runningtitle{MULTILINEAR VOLTERRA INTEDGRAL EQUATIONS} \runningauthor{{I. I. IVANOV, P. P. PETROV}} \begin{abstract} In this paper the author gives an overview of the recent results in the theory and numerical methods for solving multilinear Volterra integral equations of the first kind...\end{abstract} \keywords{majorant equation; Lambert function; nonlinear integral inequalities; Sharp estimates, numerical methods.} \end{opening} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \avtogl{I. Ivanov, P. Petrov} {Multilinear Volterra integral equations of type I elements of the theory and numerical methods} \section{Introduction} \section{Specificity of multilinear Volterra equations of the first kind } In (4) $ N = 1,2 , $ 3, we write the series %определение \begin{definition}The text of the definition \end{definition} $\bar{x}$ 123456789 %теорема \begin{theorem} The statement of the theorem \ilabel{vipeq3} %метка для теоремы \end{theorem} %доказательство \begin{proof} The text of the proof \end{proof} Based on the theorem \iref {vipeq3} we obtain \begin{theorem} The statement of the theorem \ilabel{vipeq4} \end{theorem} Based on the theorem \iref {vipeq4} we obtain %%%%%%%%%%%%%% теорема без номера \begin{theorem*} The text of the unnumbered theorem \end{theorem*} \begin{equation} x+y^2=\ln x\ilabel{vipeq1} \end{equation} Substituting in the \iref {vipeq1} instead of $ x $ variable $ y $ we obtain \begin{equation} y+y^2=\ln y\ilabel{vipeq2} \end{equation} By the formula \iref {vipeq2} %\lemma \begin{lemma} The text of the lemma \end{lemma} %\lemma без номера \begin{lemma*} unnumbered lemma \end{lemma*} \begin{state} The text of the statement \end{state} \begin{proposition} The text of the proposition \end{proposition} \begin{corollary} The text of the corollary \end{corollary} % замечание \begin{remark} The text of the remark \ilabel{vipre1} \end{remark} Given the remark \iref{vipre1} Thus, even in the case of constant kernels continuous solution of the bilinear equation exists ... \section{Majorant equation (bilinear case)} Using the notation of ~ \cite{T1975,aYa1952} ... \bigskip \section{Conclusion} We recommend using the following samples for references. The list of references should be in alphabetical order. Please use the Crossref DOI URL as the permanent link \begin{thebibliography}{999} \bibitem{Kr1965} Krni\'c L. Types of Bases in the Algebra of Logic. \textit{Glasnik Matematicko-Fizicki i Astronomski}, ser 2, 1965, vol. 20, pp. 23-32. \bibitem{L2008}Lau D., Miyakawa M. Classification and enumerations of bases in $P_k(2)$. \textit{Asian-European Journal of Mathematics}, June 2008, vol. 1, no. 2, pp. 255-282. \bibitem{M1990} Miyakawa M., Rosenberg I., Stojmenovi\'c I. Classification of Three-valued logical functions preserving 0. \textit{Discrete Applied Mathematics}, 1990, vol. 28, pp. 231-249. https://doi.org/10.1016/0166-218X(90)90005-W \end{thebibliography} \bigskip %Сведения об авторе на языке статьи \textbf{Ivan Ivanov}, Doctor of Science (Physics and Mathematicks), Professor, Institute of mathematics, economics and informatics, Irkutsk State University, 664000, Irkutsk, K. Marks str., 1, tel.:+7(3952)242210\\ \email{avtor@math.isu.ru} \textbf{Petr Petrov}, Candidate of Science (Physics and Mathematicks), Asso\-ciate Professor, Institute of mathematics, economics and informatics, Novo\-si\-birsk State University, 664000, Novo\-si\-birsk, Pirogova str., 1,\\ tel.:+7 (383)3634333 \email{petrov@math1.isu.ru} % Информация на английском языке, если статья на русском языке и на русском, если статья на английском %название \naze{Полилинейные интегральные уравнения Вольтерра I рода: элементы теории и численные методы} %авторы \avtore{И. И. Иванов} \inst{Иркутский государственный университет, Иркутск, Российская Федерация} \avtore{П. П. Петров} \inst{Новосибирский государственный университет, Новосибирск, Российская Федерация} %аннотация, \begin{abstracte} В статье дан обзор результатов, полученных авторами в последние годы в области теории и численных методов решения полилинейных интегральных уравнений Вольтерра I рода... \end{abstracte} %ключевые слова \keywordse{мажорантные уравнения; функция Ламберта; нелинейные интегральные неравенства; неулучшаемые оценки; численные методы.} \selectlanguage{russian} %список литературы \begin{bibliographyl}{999} \bibitem{Kr1965} Krni\'c L. Types of Bases in the Algebra of Logic //Glasnik Matematicko-Fizicki i Astronomski. ser. 2, 1965. Vol. 20. P. 23-32. \bibitem{L2008}Lau D., Miyakawa M. Classification and enumerations of bases in $P_k(2)$ //Asian-European Journal of Mathematics. June 2008. Vol. 1, № 2. P. 255-282. \bibitem{M1990} Miyakawa M., Rosenberg I., Stojmenovi\'c I. Classification of Three-valued logical functions preserving 0//Discrete Applied Mathematics. 1990. Vol. 28. P. 231-249. https://doi.org/10.1016/0166-218X(90)90005-W \end{bibliographyl} %Сведения об авторах \textbf{Иван Иванович Иванов}, доктор физико-математических наук, профессор, Иркутский государственный университет, Российская федерация, 664000, Иркутск, ул. К. Маркса, 1 тел.: +7(3952)242210\\ \email{avtor@math.isu.ru} %\selectlanguage{russian} \textbf{Петр Петрович Петров}, кандидат физико-математических наук, Новосибирский государственный университет, Российская федерация, 630090, Новосибирск, ул. Пирогова, 1 тел.:+7 (383)3634333\\ \email{avtor@math.isu.ru} \end{article} \end{document}