Geodesic
On a minimization problem for a functional generated by the Sturm–Liouville problem with integral condition on the potential
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 57-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we consider the minimization problem of the functional $R[Q,y]=\frac{\int_{0}^{1}y'^2dx- \int_{0}^{1}Q(x)y^2dx}{\int_{0}^{1}y^2dx}$ generated by a Sturm–Liouville problem with Dirichlet boundary conditions and with an integral condition on the potential. Estimation of the infimum of functional in some class of functions $y$ and $Q(x)$ is reduced to estimation of a nonlinear functional non depending on the potential $Q(x)$. This leads to related parameterized nonlinear boundary value problem. Upper and lower estimates for $\inf_{y\in H_{0}^{1}(0,1)}R[Q,y]$ are obtained for different values of parameter.
Keywords: variational problem, minimization of a functional, extremal estimates, spectral theory.
Mots-clés : problem of Sturm–Liouville, infimum 
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     title = {On a minimization problem for a functional generated by the {Sturm{\textendash}Liouville} problem with integral condition on the potential},
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S. S. Ezhak. On a minimization problem for a functional generated by the Sturm–Liouville problem with integral condition on the potential. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2015), pp. 57-61. http://geodesic.mathdoc.fr/item/VSGU_2015_6_a6/

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