Periodic Solutions of Parabolic Equations with Hysteresis in Dimension 1

Enin, Aleksandr; Perstneva, P. S.; Tikhomirov, Sergey

doi:10.1007/s10958-021-05670-2

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2023

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Cited by 1 publication

(2 citation statements)

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“…Recently, a county of investigation with respect to the boundary value problems with hysteresis type is increased. In the paper [1], the existence and stability of unimodal periodic solutions of the heat equation on the interval with nonideal relay was studied. Wherein, the nonideal relay was modelled by the hysteresis type boundary condition.…”

Section: Introductionmentioning

confidence: 99%

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Sturm-Liouville operator with an incomplete system of eigenfunctions and having a finite incompleteness defect

Kanguzhin,

Nurakhmetov,

Aniyarov

2023

Preprint

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In this paper, we study one Sturm-Liouville problem with a nonlinear boundary condition that depends on a parameter. Depending on the value of the boundary parameter, eigenvalue problems can arise with complete, incomplete, and overflowing systems of eigenfunctions in the functional space L2[0, 1]. An example of a Sturm-Liouville operator with an incomplete system of eigenfunctions is given and the finite defect of incompleteness is calculated. Also it is given, the system of eigenfunctions of which has an excess equal to minus one. The interval of variation of the boundary parameter is found for which the system of eigenfunctions of the Sturm-Liouville operator is complete.

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Section: Introductionmentioning

confidence: 99%

“…Then the length of the vertical line, where the right end of string, will be change with the value of y ′ (0). It turns out that the indicated modification of problem (1) has an unexpected effect: for some right-hand sides of F (x), problem (1) does not have a solution. At the same time, according to the results of [4],…”

Section: Introductionmentioning

confidence: 99%