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On the existence of nonnegative radial solutions for p-Laplacian elliptic systems

100%

Jiang D. , Liu H.

1999

tom 71

nr 1

19-29

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.

Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

100%

Kong L. , Jiang D.

1998

tom 69

nr 3

265-270

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 $±10^{-7}$.

A monotone method for constructing extremal solutions to second order periodic boundary value problems

100%

Jiang D. , Kong L.

2001

tom 76

nr 3

279-286

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).

A generalized periodic boundary value problem for the one-dimensional p-Laplacian

100%

Jiang D. , Wang J.

tom 65

nr 3

265-270

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.

Multiplicity of positive solutions to second order differential equations with Neumann boundary conditions

80%

Chu J. , Jiang D. , O'Regan D. , Agarwal R.

Applicationes Mathematicae

2005

tom 32

nr 3

293-303

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.

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

80%

Jiang D. , Xu X. , O'Regan D. , Agarwal R.

2003

tom 81

nr 3

237-259

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.