Some new results concerning a class of third-order differential equations

Akhmetkaliyeva, Raya D.; Persson, Lars‐Erik; Ospanov, Kordan N.; Wall, Peter

doi:10.1080/00036811.2014.898375

Cited by 6 publications

(4 citation statements)

References 8 publications

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“…In [18], the regularity estimate was applied to the study of nonlinear Schrödinger equation. In the case n = 1, the correctness of equation ( 1) with a rapidly growing drift was shown in [19] (see also [20][21][22]).…”

Section: Introduction and Formulation Of The Resultsmentioning

confidence: 88%

Well posedness for one class of elliptic equations with drift

Ospanov

2023

Bound Value Probl

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We studied one class of second-order elliptic equations with intermediate coefficient and proved that the semi-periodic problem on a strip is unique solvable in Hilbert space. We assume that the intermediate coefficient of the equation is continuously differentiable and grows rapidly near infinity, for example, it grows faster than $(|x|+1 ) \ln (|x|+3)$ ( | x | + 1 ) ln ( | x | + 3 ) . However, we do not impose bounds on its derivatives. We believe that the lower-order coefficient is continuous, can be unlimited and change sign.

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Section: Introduction and Formulation Of The Resultsmentioning

confidence: 88%

Well posedness for one class of elliptic equations with drift

Ospanov

2023

Bound Value Probl

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“…We note that the coercive estimate problem for a solution of the two‐term equation

ly = - y^{'''} + qy = f (x),

where

q (x)

is continuous and

∣ q (x) ∣ \geq δ > 0

was considered in numerous works (see previous works [8, 9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

“…If the operator

r (x) \frac{d}{italicdx}

is a small perturbation of

A = - \frac{d^{3}}{{dx}^{3}} + q (x) E

(

E

is the identity operator), then properties of () are same as those of equation () and the methods of [8, 9] can be extended to (). In the other cases, Equation () has rarely studied.…”

Section: Introductionmentioning

confidence: 99%

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The maximal regularity of the third‐order differential equation and its applications

Ospanov,

Ospanov

2024

Math Methods in App Sciences

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In this work, we study the solvability and maximal regularity questions for the singular third‐order differential equation with unbounded coefficients and some applications. Unlike previously studied cases, the leading and intermediate coefficients of this equation can grow independently. We obtain sufficient coefficient conditions for correctness of this equation and compactness for inverse of the corresponding differential operator. We also prove the maximal regularity estimate for a generalized solution. Using these results, we obtain upper and lower estimates for the number of Kolmogorov ‐diameters of the set associated with the linear Korteweg–de Vries equation's solutions. We give an example and show that from the above inequalities follow two‐sided estimates of the Kolmogorov ‐diameters.

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On Solvability of Third-Order Singular Differential Equation

Akhmetkaliyeva

2017

Springer Proceedings in Mathematics &Amp; Statistics

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Some new results concerning a class of third-order differential equations

Cited by 6 publications

References 8 publications

Well posedness for one class of elliptic equations with drift

Well posedness for one class of elliptic equations with drift

The maximal regularity of the third‐order differential equation and its applications

On Solvability of Third-Order Singular Differential Equation

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