The limit circle and limit point criteria for second-order linear difference equations

Chen, Jingnian; Shi, Yuming

doi:10.1016/s0898-1221(04)90080-6

Cited by 24 publications

(15 citation statements)

References 7 publications

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“…Subsequently, his work was further developed (cf. [2,3,9,10], [12]- [14]). Recently, some Weyl-Titchmarsh fundamental theory of singular linear discrete Hamiltonian systems was established [4,12].…”

Section: 0} P(t) = −C(t) a * (T) A(t) B(t)mentioning

confidence: 99%

The defect index of singular symmetric linear difference equations with real coefficients

Ren

Shi

2010

Proc. Amer. Math. Soc.

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Abstract. This paper is concerned with the defect index of singular symmetric linear difference equations of order 2n with real coefficients and one singular endpoint. We show that their defect index d satisfies the inequalities n ≤ d ≤ 2n and that all values of d in this range are realized. This parallels the well known result of Glazman for differential equations established about 1950. In addition, several criteria of the limit point and strong limit point cases are established.

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Section: 0} P(t) = −C(t) a * (T) A(t) B(t)mentioning

confidence: 99%

The defect index of singular symmetric linear difference equations with real coefficients

Ren

Shi

2010

Proc. Amer. Math. Soc.

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“…Subsequently, his study was further developed (cf. [10][11][12][13]). Sun studied the number of linearly independent square summable solutions of secondorder symmetric difference equations with complex coefficients [14].…”

Section: 0} P(t) = −C(t) a * (T) A(t) B(t)mentioning

confidence: 99%

Defect indices of singular symmetric linear difference equations with complex coefficients

Ren

2012

Adv Differ Equ

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This article is concerned with the defect indices of singular symmetric linear difference equations of order 2n with complex coefficients and one singular endpoint. We first show that the positive and negative defect indices d + and d -of a class of singular symmetric linear difference equations of order 2n with complex coefficients satisfy the inequalities n ≤ d + = d -≤ 2n and all values of this range are realized. This extends the result for difference equations with real coefficients. In addition, some sufficient conditions for the limit point and the strong limit point cases are given.

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“…Some other sufficient and some sufficient and necessary conditions for the limit point and limit circle cases of scalar second-order difference equations were given later (cf. [2,3,12,13,16]). More recently, some sufficient and several sufficient and necessary conditions for the limit point and limit circle cases of scalar secondorder difference equations with complex coefficients were given in [22].…”

Section: Remark 11mentioning

confidence: 99%

“…(1.4) with d = 1 is in l.p.c. at t = ∞ by the relevant theorems of [1,2,13,16,22] under the assumptions of Corollary 3.3.…”

Section: Remark 32mentioning

confidence: 99%

Strong limit point criteria for a class of singular discrete linear Hamiltonian systems

Sun¹,

Shi²

2007

Journal of Mathematical Analysis and Applications

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This paper is concerned with the limit point case for a class of singular discrete linear Hamiltonian systems. The limit point case is divided into the strong and the weak limit point cases. Several sufficient conditions for the strong limit point case are established. In consequence, two criteria of the strong limit point case for second-order formally self-adjoint vector difference equations are obtained.

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The limit circle and limit point criteria for second-order linear difference equations

Cited by 24 publications

References 7 publications

The defect index of singular symmetric linear difference equations with real coefficients

The defect index of singular symmetric linear difference equations with real coefficients

Defect indices of singular symmetric linear difference equations with complex coefficients

Strong limit point criteria for a class of singular discrete linear Hamiltonian systems

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