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• W4311365477 abstract "By a node of a Sturm–Liouville problem, it means an interior zero of an eigenfunction. In this paper, by considering the unique node of the second Dirichlet eigenfunction as a nonlinear functional of potential from the Lebesgue space , we will study the optimization problems to minimize or to maximize subject to the constraint . By applying the recent results on the differentiability and complete continuity of in , it will be proved that for the case , these optimization problems are attained by some potentials. Moreover, a critical equation for optimizers will be derived. Finally, by considering the limit case , it will be found that the optimizers for the optimization problems for the case are certain Dirac measures. These results are then used to deduce the optimal locations of nodes ." @default.
• W4311365477 created "2022-12-25" @default.
• W4311365477 creator A5014530665 @default.
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• W4311365477 date "2022-12-13" @default.
• W4311365477 modified "2023-10-02" @default.
• W4311365477 title "A variational approach to the optimal locations of the nodes of the second Dirichlet eigenfunctions" @default.
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• W4311365477 doi "https://doi.org/10.1002/mma.8930" @default.
• W4311365477 hasPublicationYear "2022" @default.
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