Basisness of Fucik eigenfunctions for the Dirichlet Laplacian

Author:

Baustian Falko,Bobkov Vladimir

Abstract

We provide improved sufficient assumptions on sequences of Fucik eigenvaluesof the one-dimensional Dirichlet Laplacian which guarantee that the corresponding Fucik eigenfunctions form a Riesz basis in \(L^2(0,\pi)\) . For that purpose, we introduce a criterion for a sequence in a Hilbert space to be a Riesz basis. For more information see https://ejde.math.txstate.edu/conf-proc/26/b1/abstr.html

Publisher

Texas State University

Subject

Analysis

Reference9 articles.

1. M. Abramowitz, I. A. Stegun; Handbook of mathematical functions with formulas, graphs, and mathematical tables, U.S. Government Printing Office, 1972.

2. F. Baustian, V. Bobkov; Basis properties of Fucik eigenfunctions, Anal. Math., 48 (2022), 619-648.

3. M. Cuesta; On the Fucik spectrum of the Laplacian and p-Laplacian, Proceedings of the “2000 Seminar in Differential Equations, Kvilda (Czech Republic), 2000.

4. E. N. Dancer; On the Dirichlet problem for weakly non-linear elliptic partial differential equations, P. Roy. Soc. Edinb. A, 76 (1977), 283-300.

5. R. J. Duffin, J. J. Eachus; Some notes on an expansion theorem of Paley and Wiener, Bull. Am. Math. Soc., 48 (1942), 850855.

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