Oscillation and nonoscillation criteria for second order quasilinear differential equations

Kusano, Takaŝi; Naito, Yūki

doi:10.1007/bf02907054

Cited by 83 publications

(58 citation statements)

References 4 publications

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“…As a first statement of this section we prove via the variational technique the following variant of Theorem 3.5 of [14] which is in [14] proved using the Riccati technique.…”

Section: Variational Principlementioning

confidence: 94%

“…Note also that the nonoscillation criterion (11) is not actually new and was proved for the first time in [15] by using the Riccati technique.…”

Section: Variational Principlementioning

confidence: 99%

“…In the last decade, considerable effort has been made to generalize the linear oscillation and nonoscillation criteria to (1), see e.g. [3,4,7,9,14,15,16,18] and the reference given therein. These investigations were mostly based on the so-called Riccati technique consisting in the fact that if y is a nonzero solution of (1) then w(t) = r(t)Φ(y ) Φ(y)…”

Section: Introductionmentioning

confidence: 99%

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Methods of oscillation theory of half-linear second order differential equations

Došlý¹

2000

Czechoslovak Mathematical Journal

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“…As a first statement of this section we prove via the variational technique the following variant of Theorem 3.5 of [14] which is in [14] proved using the Riccati technique.…”

Section: Variational Principlementioning

confidence: 94%

“…Note also that the nonoscillation criterion (11) is not actually new and was proved for the first time in [15] by using the Riccati technique.…”

Section: Variational Principlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Methods of oscillation theory of half-linear second order differential equations

Došlý¹

2000

Czechoslovak Mathematical Journal

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“…If T ¼ Z, system (20) is reduced to a Emden-Fowler system of difference equations while it is reduced to a Emden-Fowler system of differential equations when T ¼ R, see Refs. [32,39,40], respectively. We also refer readers to Refs.…”

Section: Emden-fowler Dynamical Systems On Time Scalesmentioning

confidence: 99%

On Nonoscillatory Solutions of Two-Dimensional Nonlinear Dynamical Systems

Akın¹,

Öztürk²

2017

Dynamical Systems - Analytical and Computational Techniques

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During the past years, there has been an increasing interest in studying oscillation and nonoscillation criteria for dynamical systems on time scales that harmonize the oscillation and nonoscillation theory for the continuous and discrete cases in order to combine them in one comprehensive theory and eliminate obscurity from both. We not only classify nonoscillatory solutions of two-dimensional systems of first-order dynamic equations on time scales but also guarantee the existence of such solutions using the Knaster, Schauder-Tychonoff and Schauder's fixed point theorems. The approach is based on the sign of components of nonoscillatory solutions. A short introduction to the time scale calculus is given as well. Examples are significant in order to see if nonoscillatory solutions exist or not. Therefore, we give several examples in order to highlight our main results for the set of real numbers R, the set of integers Z and q N 0 = {1, q, q 2 , q 3 , …}, q >1, which are the most well-known time scales.

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“…For instance, they are frequently used for the study of distributed networks containing lossless transmission lines;see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In the last decades, there are many studies that have been made on the oscillatory behavior of solutions of second and first differential equations.…”

Section: Introductionmentioning

confidence: 99%