2013
DOI: 10.1216/rmj-2013-43-5-1521
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Existence of nonoscillatory solutions to second-order nonlinear neutral dynamic equations on time scales

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Cited by 19 publications
(30 citation statements)
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“…Some results for existence of oscillatory and nonoscillatory solutions to various classes of neutral functional dynamic equations were presented in [9,10,[13][14][15][17][18][19][20][21][22], and some open problems were given in Mathsen et al [18]. Zhu and Wang [22] studied the existence of nonoscillatory solutions to a class of first-order dynamic equations.…”
Section: Definition 11mentioning
confidence: 99%
See 1 more Smart Citation
“…Some results for existence of oscillatory and nonoscillatory solutions to various classes of neutral functional dynamic equations were presented in [9,10,[13][14][15][17][18][19][20][21][22], and some open problems were given in Mathsen et al [18]. Zhu and Wang [22] studied the existence of nonoscillatory solutions to a class of first-order dynamic equations.…”
Section: Definition 11mentioning
confidence: 99%
“…Zhu and Wang [22] studied the existence of nonoscillatory solutions to a class of first-order dynamic equations. Gao and Wang [10] considered the same problem of a second-order dynamic equation…”
Section: Definition 11mentioning
confidence: 99%
“…∆ + f (t, x (h(t))) = 0 on a time scale T. Gao and Wang [12] investigated a second-order nonlinear neutral dynamic equation r(t)(x(t) + p(t)x (g(t))) ∆ ∆ + f (t, x (h(t))) = 0 (1.1)…”
Section: [X(t) + P(t)x (G(t))]mentioning
confidence: 99%
“…In this paper, we further consider (1.2) on a time scale T satisfying sup T = ∞, where t ∈ [t 0 , ∞) T = [t 0 , ∞) ∩ T with t 0 ∈ T. The motivation originates from [10,12,20,23,24]. We shall establish the existence of nonoscillatory solutions to (1.2) by employing Krasnoselskii's fixed point theorem, and we will give three examples to show the versatility of the results.…”
Section: [X(t) + P(t)x (G(t))]mentioning
confidence: 99%
“…In this paper, we consider the existence of nonoscillatory solutions to fourth-order nonlinear neutral dynamic equations of the form r 1 (t) r 2 (t) r 3 (t) x(t) + p(t)x g (t) + f t, x h(t) = 0 (1) on a time scale T satisfying sup T = ∞, where t ∈ [t 0 , ∞) T with t 0 ∈ T. The oscillation and nonoscillation of nonlinear differential and difference equations have been developed rapidly in the recent decades. Afterwards, the theory of time scale united the differential and difference ones, and since then many researchers have investigated the oscillation and nonoscillation criteria of nonlinear dynamic equations on time scales; see, for instance, the papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references cited therein. The majority of the scholars obtained the sufficient conditions to ensure that the solutions of the equations oscillate or tend to zero by using the generalized Riccati transformation and integral averaging technique.…”
Section: Introductionmentioning
confidence: 99%