Bounds for Eigenvalues of the p-Laplacian with Weight Function of Bounded Variation

被引：1

作者：

Binding, P. A. ^{[1
]}

Volkmer, H. ^{[2
]}

机构：

[1] Univ Calgary, Dept Math & Stat, Univ Dr NW, Calgary, AB T2N 1N4, Canada

[2] Univ Wisconsin Milwaukee, Dept Math Sci, Milwaukee, WI 53201 USA

来源：

TOPICS IN OPERATOR THEORY, VOL 2: SYSTEMS AND MATHEMATICAL PHYSICS | 2010年 / 203卷

关键词：

p-Laplacian; eigenvalue bounds; Prufer angle; total variation; Kronecker's theorem; ASYMPTOTIC-BEHAVIOR;

D O I：

10.1007/978-3-0346-0161-0_4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Prufer angle methods are used to establish bounds for eigenvalues of the equation -(vertical bar y'vertical bar(p-2)y')' = lambda(p - 1)r(x)vertical bar y vertical bar(p-2) involving the p-Laplacian. The bounds are expressed in terms of a generalized total variation of the coefficient r. An application of Kronecker's theorem shows that the bounds are optimal in generic cases.

引用

页码：99 / +

页数：3

共 16 条

[1]

Binding P, 2003, STUD SCI MATH HUNG, V40, P375

[2] Oscillation and interlacing for various spectra of the p-Laplacian [J].

Binding, Paul A. ;

Rynne, Bryan P. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (7-8) :2780-2791

[3] Asymptotic behavior of the eigenvalues of the one-dimensional weighted p-Laplace operator [J].

Bonder, JF ;

Pinasco, JP .

ARKIV FOR MATEMATIK, 2003, 41 (02) :267-280

[4] Titchmarsh's asymptotic formula for periodic eigenvalues and an extension to the p-Laplacian [J].

Brown, B. M. ;

Eastham, M. S. P. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) :1255-1266

[5] Maps of bounded variation with values in a metric space [J].

Chistyakov, VV .

RUSSIAN MATHEMATICAL SURVEYS, 1999, 54 (03) :630-631

[6]

Eastham M.S.P., 1975, LECT NOTES MATH, V448, P126

[7]

Eberhard W, 2000, MATH NACHR, V213, P57, DOI 10.1002/(SICI)1522-2616(200005)213:1<57::AID-MANA57>3.0.CO

[8]

2-J

[9]

ELBERT A, 1979, QUALITATIVE THEORY D, P153

[10] ASYMPTOTIC-BEHAVIOR OF THE EIGENVALUES OF THE P-LAPLACIAN [J].

FRIEDLANDER, L .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1989, 14 (8-9) :1059-1069

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