Sturm–Liouville problems with indefinite weights and Everitt's inequality

Volkmer, Hans

doi:10.1017/s0308210500023283

Cited by 40 publications

(54 citation statements)

References 12 publications

(19 reference statements)

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“…the real spectrum of A necessarily accumulates to +∞ and −∞ and A may have non-real eigenvalues which possibly accumulate to the real axis (see [3,4,9,14,16,20]). For further indefinite Sturm-Liouville problems, applications and references, see, e.g., [2,6,7,11,13,15,23,26].…”

Section: Introductionmentioning

confidence: 99%

Non-real eigenvalues of singular indefinite Sturm-Liouville operators

Behrndt

Katatbeh

Trunk

2009

Proc. Amer. Math. Soc.

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Abstract. We study a Sturm-Liouville expression with indefinite weight of the form sgn(−d 2 /dx 2 + V ) on R and the non-real eigenvalues of an associated selfadjoint operator in a Krein space. For real-valued potentials V with a certain behaviour at ±∞ we prove that there are no real eigenvalues and that the number of non-real eigenvalues (counting multiplicities) coincides with the number of negative eigenvalues of the selfadjoint operator associated toThe general results are illustrated with examples.

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Section: Introductionmentioning

confidence: 99%

Non-real eigenvalues of singular indefinite Sturm-Liouville operators

Behrndt

Katatbeh

Trunk

2009

Proc. Amer. Math. Soc.

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“…To conclude this introduction we remark that our conditions simplify drastically if p is even and r is odd, a case which has been studied by several authors [6,17,22]. In fact all the conditions that we impose on the boundary are then equivalent; see Example 4.3 and Corollary 6.5.…”

Section: Introductionmentioning

confidence: 86%

Riesz Bases of Root Vectors of Indefinite Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions. II

Binding

Ćurgus

2009

Integr. equ. oper. theory

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Abstract. We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this SturmLiouville problem can be selected to form a Riesz basis of a corresponding weighted Hilbert space. Mathematics Subject Classification (2000). Primary: 34B05, 47B50. Secondary: 34B09, 34B25, 47B25.

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“…[4]) on the weight function is necessary (cf. [15]). We also show that completeness may fail for such problems in H a .…”

Section: )mentioning

confidence: 99%