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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 .”