A class of nonlocal indefinite differential systems

Li, Ping; Feng, Meiqiang; Qin, Peige

doi:10.1186/s13661-018-1000-4

Cited by 2 publications

(2 citation statements)

References 51 publications

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“…Problems with integral boundary conditions come naturally from thermal conduction problems [29] and hydrodynamic problems [30]. In recent years there has been a lot of investigation of boundary value problems with integral boundary conditions (see for instance [31][32][33][34][35][36][37][38][39][40][41][42][43]). In particular, Boucherif [44] used the fixed point theorem in cones to consider the following problem: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ u (t) = f (t, u(t)), 0 < t < 1, u(0)cu (0) = 1 0 g 0 (t)u(t) dt, u(1)du (1) = 1 0 g 1 (t)u(t) dt.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Zhang

2019

Bound Value Probl

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In this paper we consider sharp conditions on ω and f for the existence of C 1 [0, 1] positive solutions to a second-order singular nonlocal problem u (t) + ω(t)f (t, u(t)) = 0, u(0) = u(1) = 1 0 g(t)u(t) dt; it turns out that this case is more difficult to handle than two point boundary value problems and needs some new ingredients in the arguments. On the technical level, we adopt the topological degree method.

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Section: Introductionmentioning

confidence: 99%

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Zhang

2019

Bound Value Probl

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“…Comparing with Li, Feng, and Qin[60], the main features of this paper are as follows:(i) p > 1is considered, not only p ≡ 2. (ii) I k = 0 (k = 1, 2, .…”

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confidence: 99%

Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems

Qin

Feng

2018

Adv Differ Equ

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Consider the one-dimensional quasilinear impulsive boundary value problem involving the p-Laplace operator ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩-(φ p (u)) = λω(t)f (u), 0 < t < 1,-u| t=t k = μI k (u(t k)), k = 1, 2,. .. , n, u | t=t k = 0, k = 1, 2,. .. , n, u (0) = 0, u(1) = 1 0 g(t)u(t) dt, where λ, μ > 0 are two positive parameters, φ p (s) is the p-Laplace operator, i.e., φ p (s) = |s| p-2 s, p > 1, ω(t) changes sign on [0, 1]. Several new results are obtained for the above quasilinear indefinite problem.

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A class of nonlocal indefinite differential systems

Abstract: We consider the solvable intervals of two positive parameters λ and μ in which the second-order nonlocal differential system

Cited by 2 publications

References 51 publications

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems

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