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1
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Multiple positive solutions to singular boundary value problems for superlinear second order FDEs

100%
Jiang D.
Annales Polonici Mathematici
|
2000
|
tom 75
|
nr 3
257-270
EN
We study the existence of positive solutions to the singular boundary value problem for a second-order FDE ⎧ u'' + q(t) f(t,u(w(t))) = 0, for almost all 0 < t < 1, ⎨ u(t) = ξ(t), a ≤ t ≤ 0, ⎩ u(t) = η(t), 1 ≤ t ≤ b, where q(t) may be singular at t = 0 and t = 1, f(t,u) may be superlinear at u = ∞ and singular at u = 0.
2
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A generalized periodic boundary value problem for the one-dimensional p-Laplacian

64%
Jiang D., Wang J.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 3
265-270
EN
The generalized periodic boundary value problem -[g(u')]' = f(t,u,u'), a < t < b, with u(a) = ξu(b) + c and u'(b) = ηu'(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, $g(s) = |s|^{p-2} s$, p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.
3
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Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

64%
Kong L., Jiang D.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 3
265-270
EN
The fourth order periodic boundary value problem $u^{(4)} - m⁴u + F(t,u) = 0$, 0 < t < 2π, with $u^{(i)}(0) = u^{(i)}(2π)$, i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $±10^{-7}$.
4
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A monotone method for constructing extremal solutions to second order periodic boundary value problems

64%
Jiang D., Kong L.
Annales Polonici Mathematici
|
2001
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tom 76
|
nr 3
279-286
EN
We describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) in the presence of a lower solution α(t) and an upper solution β(t) with β(t) ≤ α(t).
5
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On the existence of nonnegative radial solutions for p-Laplacian elliptic systems

64%
Jiang D., Liu H.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 1
19-29
EN
The existence of nonnegative radial solutions for some systems of m (m ≥ 1) quasilinear elliptic equations is proved by a simple application of a fixed point theorem in cones.
6
Content available remote

Existence theory for single and multiple solutions to singular positone boundary value problems for the delay one-dimensional p-Laplacian

51%
Jiang D., Xu X., O'Regan D., Agarwal R.
Annales Polonici Mathematici
|
2003
|
tom 81
|
nr 3
237-259
EN
The existence of single and multiple nonnegative solutions for singular positone boundary value problems to the delay one-dimensional p-Laplacian is discussed. Throughout our nonlinearity f(·,y) may be singular at y = 0.
7
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Multiplicity of positive solutions to second order differential equations with Neumann boundary conditions

51%
Chu J., Jiang D., O'Regan D., Agarwal R.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 3
293-303
EN
We study the existence of positive solutions to second order nonlinear differential equations with Neumann boundary conditions. The proof relies on a fixed point theorem in cones, and the positivity of Green's function plays a crucial role in our study.
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