Second order q-difference equations solvable by factorization method

Dobrogowska, Alina; Odzijewicz, Anatol

doi:10.1016/j.cam.2005.06.009

Cited by 80 publications

(40 citation statements)

References 15 publications

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“…In recent years, the topic of q-calculus has attracted the attention of several researchers and a variety of new results can be found in the papers [1], [2], [3], [4], [5], [6], [8], [9], [10], [11], [12], [18], [19] and the references cited therein.…”

Section: Theorem 15 ([17]mentioning

confidence: 99%

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE q_k-DIFFERENCE EQUATIONS

Ntouyas¹,

Tariboon²,

Thiramanus³

2016

Bulletin of the Korean Mathematical Society

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Abstract. Based on the notion of q k -derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive q k -difference equations with antiperiodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.

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Section: Theorem 15 ([17]mentioning

confidence: 99%

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE q_k-DIFFERENCE EQUATIONS

Ntouyas¹,

Tariboon²,

Thiramanus³

2016

Bulletin of the Korean Mathematical Society

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“…The study of q-difference equations, initiated in the beginning of the 20th century ( [1][2][3][4]), and, up to date, it has evolved into a multidisciplinary subject, (for example, see ( [5][6][7][8][9][10][11][12][13][14][15]) and references therein). For some recent work on q-difference equations, we refer the reader to the papers ( [16][17][18][19][20][21][22][23]). However, the theory of boundary value problems for nonlinear q-difference equations is still in the initial stage and many aspects of this theory need to be explored.…”

Section: U(t) = F (T U(t)) T ∈ I U(0) = ηU(t) D Q U(0) = ηD Q U(t)mentioning

confidence: 99%

A study of second-order q-difference equations with boundary conditions

2012

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This paper studies a boundary value problem of nonlinear second-order q-difference equations with non-separated boundary conditions. As a first step, the given boundary value problem is converted to an equivalent integral operator equation by using the q-difference calculus. Then the existence and uniqueness of solutions of the problem is proved via the resulting integral operator equation by means of Leray-Schauder nonlinear alternative and some standard fixed point theorems. Our approach is simpler than the one involving the typical series solution form of qdifference equations. The results corresponding to a second-order q-difference equation with anti-periodic boundary conditions appear as a special case. Furthermore, our results reduce to the corresponding results for classical secondorder boundary value problems with non-separated boundary conditions in the limit q 1, which provides a useful check.

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“…The book by Kac and Cheung [14] covers many of the fundamental aspects of quantum calculus. A variety of new results can be found in the papers [2,3,4,5,6,7,8,11,12,24,25,26,27] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for nonlinear impulsive qk -difference equations with first-order qk -derivatives

Yu¹,

Wang²,

Guo³

2016

J. Nonlinear Sci. Appl.

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In this paper, we study the nonlinear second-order impulsive q k -difference equations with Sturm-Liouville type, in which nonlinear team and impulsive teams are dependent on first-order q k -derivatives. We obtain the existence and uniqueness results of solutions for the problem by Banach's contraction mapping principle and Schaefer's fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. c 2016 All rights reserved.Keywords: q k -derivative, q k -integral, impulsive q k -difference equation, boundary value problem, fixed point theorem. 2010 MSC: 39A13, 34B15, 34B37, 81Q99.

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Second order q-difference equations solvable by factorization method

Cited by 80 publications

References 15 publications

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE q_k-DIFFERENCE EQUATIONS

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE q_k-DIFFERENCE EQUATIONS

A study of second-order q-difference equations with boundary conditions

Existence of solutions for nonlinear impulsive qk -difference equations with first-order qk -derivatives

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Second order q-difference equations solvable by factorization method

Cited by 80 publications

References 15 publications

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE qk-DIFFERENCE EQUATIONS

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE qk-DIFFERENCE EQUATIONS

A study of second-order q-difference equations with boundary conditions

Existence of solutions for nonlinear impulsive qk -difference equations with first-order qk -derivatives

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Product

Resources

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EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE q_k-DIFFERENCE EQUATIONS

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE q_k-DIFFERENCE EQUATIONS