Renewal equation on the whole line

Yengibarian, N. B.

doi:10.1016/s0304-4149(99)00076-9

Cited by 21 publications

(14 citation statements)

References 9 publications

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“…We notice that Engibaryan [30] has shown that under the hypotheses of Karlin's theorem the boundedness of g is a necessary and sufficient condition for the existence of a bounded solution of (2.14).…”

mentioning

confidence: 87%

Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

Khachatryan¹

2015

Izv. Math.

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We study certain classes of non-linear Hammerstein integral equations on the semi-axis and the whole line. These classes of equations arise in the theory of radiative transfer in nuclear reactors, in the kinetic theory of gases, and for travelling waves in non-linear Richer competition systems. By combining special iteration methods with the methods of construction of invariant cone segments for the appropriate nonlinear operator, we are able to prove constructive existence theorems for positive solutions in various function spaces. We give illustrative examples of equations satisfying all the hypotheses of our theorems.

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confidence: 87%

Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line

Khachatryan¹

2015

Izv. Math.

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“…Если п = 1, то (1.1) представляет собой уравнение восстановления (УВ) на всей прямой (см. [1]- [5]). …”

Section: )unclassified

“…Эти методы более действенны в вопросах един ственности. В настоящей работе, с помощью результатов работы автора [5] по У В на всей прямой, простыми средствами будут получены результаты по разрешимо сти и свойствам решений уравнения (1.1), (1.2). Вводится специальный класс функ ций, в котором устанавливается существование и единственность решения УВМП при д G Li(R n ) и наличии конечного первого момента у К. В разделе б этим результа там дается простая вероятностная интерпретация на примере одного стохастического процесса.…”

Section: )unclassified

Уравнение Восстановления В Многомерном Пространстве

Енгибарян¹,

Engibaryan²

2004

Teor. Veroyatnost. i Primenen.

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“…So the asymptotic properties of the solution to (5.1) are those of the convolution g * H(t), which, under various assumptions, have been studied by several authors [12,13,8,2,1]. Some properties of X(t) were later rediscovered in a slightly more general setting [15,Theorem 5.1]. Usually, assertions about the asymptotic behavior of g * H(t) are called key renewal theorems.…”

Section: Convergence Rates In a Key Renewal Theoremmentioning

confidence: 99%