1912
DOI: 10.1090/s0002-9947-1912-1500902-8
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Theorems of oscillation for two linear differential equations of the second order with two parameters

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Cited by 54 publications
(27 citation statements)
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“…We shall prove the theorem by the method of eigencurves (see [11] and [12]), and hence before beginning the proof we shall have to establish some information concerning each of the systems (2.2)-(2.3) and (2.4)-(2.5).…”
Section: Assumption 31 Together With (22) and (24) Assure Us That mentioning
confidence: 99%
“…We shall prove the theorem by the method of eigencurves (see [11] and [12]), and hence before beginning the proof we shall have to establish some information concerning each of the systems (2.2)-(2.3) and (2.4)-(2.5).…”
Section: Assumption 31 Together With (22) and (24) Assure Us That mentioning
confidence: 99%
“…The (local) indefinite Sturm-Liouville problem, i.e., K(x, t) = 0 in (1.1) with self-adjoint boundary conditions, has discrete, real eigenvalues unbounded from both below and above, and may also admit non-real eigenvalues (see [3,16,18,29]). The indefinite nature was noticed by Haupt [13], Richardson [24] at the beginning of the last century and has attracted a lot of attention in recent years. Determining a priori bounds and determining the exact number of non-real eigenvalues are an interesting and difficult problems in Sturm-Liouville theory.…”
Section: Introductionmentioning
confidence: 99%
“…In this paper we consider the eigenvalue problem associated with the singular indefinite Sturm-Liouville differential expression − (py ) + qy = λwy in L 2 |w| (a, b), (1.1) where −∞ a < b ∞, the functions p, q, w are real-valued and w changes sign on (a, b). Such a problem is called indefinite and the indefinite nature, that nonreal spectral points may appear, was noticed by Haupt [11], Richardson [19] at the beginning of the last century and has attracted a lot of attention in the recent years, see [1,2,[8][9][10]14]. For a review of early works on indefinite problems, see [15].…”
Section: Introductionmentioning
confidence: 99%