The convective eigenvalues of the one-dimensional p-Laplacian as p → 1

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

de la Calle Ysern, B.¹  Sabina de Lis, J. C.^2,3  Segura de Leon, S.⁴ 

[1] Univ Politecn Madrid, Dept Matemat Aplicada & Ingn Ind, Jose Gutierrez Abascal 2, E-28006 Madrid, Spain

[2] Univ La Laguna, Dept Anal Matemat, POB 456, San Cristobal la Laguna 38200, Spain

[3] Univ La Laguna, IUEA, POB 456, San Cristobal la Laguna 38200, Spain

[4] Univ Valencia, Dept Anal Matemat, Dr Moliner 50, E-46100 Valencia, Spain

关键词: Eigenvalues and eigenfunctions;    One-dimensional p-Laplacian operator;    One-dimensional 1-Laplacian operator;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2019.123738

来源: Elsevier

【 摘 要 】

This paper studies the limit behavior as p > 1 of the eigenvalue problem {-vertical bar u(x)vertical bar(p-2)u(x))(x) - c vertical bar u(x)vertical bar(p-2)u(x) = lambda vertical bar u vertical bar(p-2)u, 0 < x < 1, u(0) = u(1) = 0. We point out that explicit expressions for both the eigenvalues lambda(n) and associated eigenfunctions are not available (see [16]). In spite of this hindrance, we obtain the precise values of the limits lim(p -> 1+) lambda(n). In addition, a complete description of the limit profiles of the eigenfunctions is accomplished. Moreover, the formal limit problem as p -> 1 is also addressed. The results extend known features for the special case c = 0 ([6], [28]). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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