Perturbed generalized half-linear Riemann–Weber equation – further oscillation results

Fišnarová, Simona; Pátíková, Zuzana

doi:10.14232/ejqtde.2017.1.69

Cited by 14 publications

(7 citation statements)

References 9 publications

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“…(a) Let us mention that Corollary 3, as the specific application of Theorem 2 to concrete Equations (20) and (17), and the generalized Riemann-Weber equation with n + 1 terms, brings a result which is in compliance with the Hille-Nehari-type criterion, that was proved in [17] (more on Hille-Nehari-type criteria for (20) can be found also in [18]). Its non-oscillatory part says the following.…”

Section: Discussionmentioning

confidence: 80%

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Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

Pátíková

2021

Mathematics

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In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations. Compared equations are seen as perturbations of a given non-oscillatory equation, which allows studying the equations on the borderline of oscillation and non-oscillation. We bring a new comparison theorem and apply it to the so-called generalized Riemann–Weber equation (also referred to as a Euler-type equation).

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Section: Discussionmentioning

confidence: 80%

“…Thus, (10) holds (the calculation can be found in [17] above the relation (3.9)). The condition in (9) is reduced to (18).…”

Section: Corollary 2 Suppose That the Conditionmentioning

confidence: 99%

Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

Pátíková

2021

Mathematics

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“…It is based on constructions published in Veselý 55 (see also studies 56‐59 in the discrete case). However, the existence of such coefficients R , S follows from results about equations with perturbations as well (see Elbert and Schneider 60 and also other studies 61‐64 ).…”

Section: Corollaries and Commentsmentioning

confidence: 81%

Non‐oscillation of linear and half‐linear differential equations with unbounded coefficients

Šišoláková

2020

Math Methods in App Sciences

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We deal with Euler-type half-linear second-order differential equations, and our intention is to derive conditions in order their non-trivial solutions are non-oscillatory. This paper connects to the article P. Hasil, J. Šišoláková, M. Veselý: Averaging technique and oscillation criterion for linear and half-linear equations, Appl. Math. Lett. 92 (2019), 62-69, where the corresponding oscillatory counterpart is studied and an oscillation criterion is established. The used effective technique for this investigation is the combination of the generalized adapted Prüfer angle and the modified Riccati transformation. This paper is completed by two corollaries and an example concerning the linear case when we obtain new results as well.

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“…For other generalizations of Theorem 2.3, we refer to [24,34,46,48], where periodic coefficients with different periods or sums of periodic functions as coefficients (see also [23,50]) are considered.…”

Section: Previous Resultsmentioning

confidence: 99%

“…Theorem 6.3 is a direct generalization of many oscillation and nonoscillation criteria. We mention at least papers [6, 7, 9–12, 16, 20, 24, 34, 43, 46–48, 61], whose main results follow from Theorem 6.3.…”

Section: Conditional Oscillationmentioning

confidence: 99%

Oscillation and nonoscillation of perturbed nonlinear equations with p‐Laplacian

Hasil

Veselý

2023

Mathematische Nachrichten

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In this paper, we analyze oscillatory properties of perturbed half-linear differential equations (i.e., equations with one-dimensional 𝑝-Laplacian). The presented research covers the Euler and Riemann-Weber type equations with very general coefficients. We prove an oscillatory result and a nonoscillatory one, which show that the studied equations are conditionally oscillatory (i.e., there exists a certain threshold value that separates oscillatory and nonoscillatory equations). The obtained criteria are easy to use. Since the number of perturbations is arbitrary, we solve the oscillation behavior of the equations in the critical setting when the coefficients give exactly the threshold value. The results are new for linear equations as well.

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Perturbed generalized half-linear Riemann–Weber equation – further oscillation results

Cited by 14 publications

References 9 publications

Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation

Non‐oscillation of linear and half‐linear differential equations with unbounded coefficients

Oscillation and nonoscillation of perturbed nonlinear equations with p‐Laplacian

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