Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 160, Pages 32–41 (Mi into422)  
On the number of solutions for a certain class of nonlinear second-order boundary-value problems

A. V. Kirichukaa, F. Zh. Sadyrbaevb

a Daugavpils University
b University of Latvia, Institute of Mathematics and Computer Science
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Abstract: The boundary-value problem for the differential equation with quadratic nonlinearity $x''=-ax+b x^2$ with the boundary conditions $x'(0)=x'(T)=0$ is is considered. The number of solutions of for the boundary-value problem is found. An illustrative example is presented.
Keywords: boundary-value problem, quadratic nonlinearity, phase trajectory, multiplicity of solutions, Jacobian elliptic function.
Bibliographic databases:
Document Type: Article
UDC: 517, 531.01
MSC: 34B15, 34C10, 34C37
Language: Russian
Citation: A. V. Kirichuka, F. Zh. Sadyrbaev, “On the number of solutions for a certain class of nonlinear second-order boundary-value problems”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 32–41
Citation in format AMSBIB
\Bibitem{KirSad19}
\by A.~V.~Kirichuka, F.~Zh.~Sadyrbaev
\paper On the number of solutions for a certain class of nonlinear second-order boundary-value problems
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 32--41
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into422}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3981828}
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