Geodesic
On the number of solutions for a certain class of nonlinear second-order boundary-value problems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 32-41

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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. 
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     author = {A. V. Kirichuka and F. Zh. Sadyrbaev},
     title = {On the number of solutions for a certain class of nonlinear second-order boundary-value problems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {32--41},
     publisher = {mathdoc},
     volume = {160},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_160_a4/}
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A. V. Kirichuka; F. Zh. Sadyrbaev. On the number of solutions for a certain class of nonlinear second-order boundary-value problems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 32-41. http://geodesic.mathdoc.fr/item/INTO_2019_160_a4/