On the convergence of the sequence of solutions for a family of eigenvalue problems | Zendy

Fărcăşeanu Maria | Zendy; Mihăilescu Mihai | Zendy; StancuDumitru Denisa | Zendy

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On the convergence of the sequence of solutions for a family of eigenvalue problems

Author(s) -

Fărcăşeanu Maria,

Mihăilescu Mihai,

StancuDumitru Denisa

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4502

Subject(s) - mathematics , eigenfunction , sequence (biology) , eigenvalues and eigenvectors , bounded function , domain (mathematical analysis) , convergence (economics) , limit of a sequence , boundary (topology) , mathematical analysis , function (biology) , class (philosophy) , boundary value problem , pure mathematics , limit (mathematics) , genetics , physics , quantum mechanics , economics , biology , economic growth , evolutionary biology , artificial intelligence , computer science

The asymptotic behavior of the sequence { u n } of positive first eigenfunctions for a class of eigenvalue problems is studied in a bounded domain Ω ⊂ R N with smooth boundary ∂ Ω. We prove u n → ‖ δ ‖L 2 ( Ω ) − 1 δ , where δ is the distance function to ∂ Ω. Our study complements some earlier results by Payne and Philippin, Bhattacharya, DiBenedetto, and Manfredi, and Kawohl obtained in relation with the “ torsional creep problem .”

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