Upper and lower solution method for nth-order BVPs on an infinite interval

Lian, Huiqin; Zhao, Junfang; Agarwal, Ravi P.

doi:10.1186/1687-2770-2014-100

Cited by 10 publications

(7 citation statements)

References 22 publications

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“…As far as we know, this technique was introduced in [33], and, originally, it was used so that the exponential function was the weighted function. Some authors still used it, as in [34], but we may use weaker weighted functions: polynomial functions, as in [35] or [26].…”

Section: Definitions and Auxiliary Resultsmentioning

confidence: 99%

“…Solutions of the linear problem associated to (1)-( 2) are defined with kernels given by Green's function, which can be obtained by standard calculus, as in [26], Lemma 2.1:…”

Section: Definitions and Auxiliary Resultsmentioning

confidence: 99%

“…In more detail, we refer to [26], where the authors study the the nth-order differential equation on the half-line −u (n) (t) = q(t) f (t, u(t), . .…”

Section: Introductionmentioning

confidence: 99%

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Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line

Minhós

Coxe²

2021

Mathematics

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In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the (n−1)th derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global assumptions on the unknown function and its derivatives, such as nonlocal, integro-differential, infinite multipoint, with maximum or minimum arguments, among others. Considering the half-line as the domain carries on a lack of compactness, which is overcome with the definition of a space of weighted functions and norms, and the equiconvergence at ∞. In the last section, an example illustrates the applicability of our main result.

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Section: Definitions and Auxiliary Resultsmentioning

confidence: 99%

“…Solutions of the linear problem associated to (1)-( 2) are defined with kernels given by Green's function, which can be obtained by standard calculus, as in [26], Lemma 2.1:…”

Section: Definitions and Auxiliary Resultsmentioning

confidence: 99%

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Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line

Minhós

Coxe²

2021

Mathematics

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“…For γ > 0 sufficiently large there exists a unique solution D to (4.7), see e.g. [12]. This D assures that Assumption 4 is fulfilled.…”

Section: It Follows By Relation (42) Thatmentioning

confidence: 89%

Boundary stabilization of non-diagonal systems by proportional feedback forms

Munteanu¹

2021

CPAA

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In this work, we are concerned with the problem of boundary exponential stabilization, in a Hilbert space H, of parabolic type equations, namely equations for which their linear parts generate analytic C 0 −semigroups. We consider the case where the projection of the linear leading operator, on a given Riesz basis of H, is non-diagonal. We do not assume that the linear operator has compact resolvent. Therefore, the Riesz basis is not necessarily an eigenbasis. The boundary stabilizer is given in a simple linear feedback form, of finite-dimensional structure, involving only the Riesz basis. To illustrate the results, at the end of the paper, we provide an example of stabilization of a fourth-order evolution equation on the half-axis.

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“…Bu konuyla ilgili en son çalışmalar [0, ∞) yarı sonsuz aralığı üzerindeki sınır değer problemleri üzerine devam etmiştir. Yapılan tüm çalışmalarda sınırlı ya da sınırlı olmayan çözümlerin varlığını belirlemek için ya bazı sabit nokta teoremleri ya da monoton iteratif teknikler kullanılmıştır [7][8][9][10][11][12][13][14]21].…”

Section: Introductionunclassified

Existence of solutions for a third-order boundary value problem with integral boundary conditions

Çetin

FİLİZ

2022

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Bu çalışmada, yarı sonsuz aralık üzerinde tanımlı üçüncü mertebeden üç noktalı integral koşullu, η∈(0,∞) sabit ve g:(0,∞)×R^(3 )⟶ R Nagumo koşullarını sağlayan bir fonksiyon olmak üzere, x'''(t)+r(t)g(t,x(t),x'(t),x'' (t))=0, t∈(0,∞), x(0)=∫_0^ηx(s)ds, x'(0)=A, x''(∞)=B sınır değer probleminin sınırlı veya sınırlı olmayan çözümlerinin varlığı ispatlanmıştır. Schäuder sabit nokta teoremi ve alt ve üst çözümler yöntemi uygulanarak istenilen sonuca ulaşılmıştır. Problemimizde uygun ve yeterli koşullar belirlenerek problemin en az bir çözümünün varlığı gösterilmiştir.

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Upper and lower solution method for nth-order BVPs on an infinite interval

Cited by 10 publications

References 22 publications

Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line

Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line

Boundary stabilization of non-diagonal systems by proportional feedback forms

Existence of solutions for a third-order boundary value problem with integral boundary conditions

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