Existence of eventually positive solutions of fourth order quasilinear differential equations

Wu, Fang

doi:10.1016/j.jmaa.2011.11.061

Cited by 11 publications

(9 citation statements)

References 6 publications

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“…The oscillation and non-oscillation of the fourth and higherorder differential equations have been the focus of the attention of numerous authors since this paper was first published. Wu [9] and Kamo and Usami [10] studied the oscillatory of a fourth-order differential equation…”

Section: Introductionmentioning

confidence: 99%

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Non-Canonical Functional Differential Equation of Fourth-Order: New Monotonic Properties and Their Applications in Oscillation Theory

Nabih

Cesarano

Moaaz

et al. 2022

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In the present article, we iteratively deduce new monotonic properties of a class from the positive solutions of fourth-order delay differential equations. We discuss the non-canonical case in which there are possible decreasing positive solutions. Then, we find iterative criteria that exclude the existence of these positive decreasing solutions. Using these new criteria and based on the comparison and Riccati substitution methods, we create sufficient conditions to ensure that all solutions of the studied equation oscillate. In addition to having many applications in various scientific domains, the study of the oscillatory and non-oscillatory features of differential equation solutions is a theoretically rich field with many intriguing issues. Finally, we show the importance of the results by applying them to special cases of the studied equation.

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Section: Introductionmentioning

confidence: 99%

“…[16] Suppose that α ≥ 1 and the differential Equation ( 8) is oscillatory or some constant λ o ∈ (0, 1). If there is a function γ ∈ C 1 ([r o , ∞), (0, ∞)) such that (9) and…”

Section: Introductionmentioning

confidence: 99%

Non-Canonical Functional Differential Equation of Fourth-Order: New Monotonic Properties and Their Applications in Oscillation Theory

Nabih

Cesarano

Moaaz

et al. 2022

Axioms

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“…The oscillatory and asymptotic behavior of nonoscillatory solutions of (E) were considered by Kamo and Usami [5], Kusano and Tanigawa [12], Kusano, Manojlović and Tanigawa [10], Manojlović and Milošević [15], Naito and Wu [16,17], Wu [21,22]. The qualitative behavior of solutions of (E) are described by means of the integrals…”

Section: Introductionmentioning

confidence: 99%

“…In [16,17,21,22] it is assumed that p satisfies P 1 = ∞, P 2 = ∞, while in [5] it is assumed that p satisfies P 1 < ∞, P 2 = ∞, and in [15] it is assumed that p satisfies P 1 < ∞, P 2 < ∞. On the other hand, Kusano, Manojlović and Tanigawa [10,12] have considered the case P 3 < ∞.…”

Section: Introductionmentioning

confidence: 99%

Existence and asymptotic behavior of intermediate type of positive solutions of fourth-order nonlinear differential equations

Djordjevic

Manojlović

2019

Filomat

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Under the assumptions that p and q are regularly varying functions satisfying conditions ∞ a t p(t) 1 α dt < ∞ and ∞ a t p(t) 1 α dt = ∞ existence and asymptotic form of regularly varying intermediate solutions are studied for a fourth-order quasilinear differential equation p(t)|x (t)| α−1 x (t) + q(t)|x(t)| β−1 x(t) = 0, α > β > 0. It is shown that under certain integral conditions there exist two types of intermediate solutions which according to their asymptotic behavior is to be divided into six mutual distinctive classes, while asymptotic behavior of each member of any of these classes is governed by a unique explicit law. dt = ∞.

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“…Kamo and Usami [10], [11], Kusano et al [14], and Wu [20] studied the oscillation of a fourth-order nonlinear differential equation…”

Section: Introductionmentioning

confidence: 99%

Oscillation of fourth-order quasilinear differential equations

Li¹,

Rogovchenko²,

Zhang³

2015

Math. Bohem.

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We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.

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Existence of eventually positive solutions of fourth order quasilinear differential equations

Cited by 11 publications

References 6 publications

Non-Canonical Functional Differential Equation of Fourth-Order: New Monotonic Properties and Their Applications in Oscillation Theory

Non-Canonical Functional Differential Equation of Fourth-Order: New Monotonic Properties and Their Applications in Oscillation Theory

Existence and asymptotic behavior of intermediate type of positive solutions of fourth-order nonlinear differential equations

Oscillation of fourth-order quasilinear differential equations

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