Geodesic
Asymptotics of the Solution of a Variational Problem on a Large Interval
Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 688-703

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The variational problem of minimizing the energy functional that results in a second-order nonlinear differential equation of pendulum type on a finite interval with natural boundary conditions is analyzed. It is shown that the number of solutions of the boundary-value problem depends on the length $L$ of the interval and unboundedly increases as $L\to\infty$. The solutions on which the energy minimum is realized converge as $L\to\infty$ to the solution of a variational problem in the class of periodic functions.
Keywords: nonlinear equations, variational problem, asymptotics.
Mots-clés : oscillations 
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     author = {L. A. Kalyakin},
     title = {Asymptotics of the {Solution} of a {Variational} {Problem} on a {Large} {Interval}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {688--703},
     publisher = {mathdoc},
     volume = {110},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a3/}
}
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L. A. Kalyakin. Asymptotics of the Solution of a Variational Problem on a Large Interval. Matematičeskie zametki, Tome 110 (2021) no. 5, pp. 688-703. http://geodesic.mathdoc.fr/item/MZM_2021_110_5_a3/