Showing papers by "Patricia J. Y. Wong published in 2000"
TL;DR: In this article, the authors generalized the Leggett-Williams theorem to Lidstone boundary value problems and proved the analogous result for difference equations, where the growth conditions are imposed on f which yield the existence of at least three symmetric solutions.
72 citations
TL;DR: In this paper, the existence of two and three positive solutions of the boundary value problem is investigated. And for special cases, the upper and lower bounds for these positive solutions are established.
Abstract: We consider the following boundary value problem (-1)ny(2n)=F(t,y), n≥ 1, t ∈ (0,1), y(2i)(0)=y(2i)(1)=0, 0≧i≧n-1. Criteria are developed for the existence of two and three positive solutions of the boundary value problem. In addition, for special cases we establish upper and lower bounds for these positive solutions. Several examples are also included to dwell upon the importance of the results obtained.
23 citations
TL;DR: In this paper, the existence of double and triple positive solutions of the boundary value problem was investigated and for special cases upper and lower bounds for these positive solutions were established for the positive solutions.
17 citations
TL;DR: In this paper, the authors considered the continuous and discrete multipoint boundary value problems, and provided lower bounds for solutions in terms of sup0 t 1 |x(t)| and maxk∈{0,···,m+n} |y(k)|.
Abstract: This paper considers the following continuous and discrete multipoint boundary value problems: x(n)(t) 0, 0 t 1, x(ti) = 0 and Δny(k) 0, k = 0, · · · , m, Δy(ki) = 0, where j = 0, · · · , ni − 1, i = 1, · · · , r, ∑r i=1 ni = n, 0 = t1 < t2 < · · · < tr = 1, and 0 = k1 < k1 + n1 < k2 < k2 + n2 < · · · < kr kr + nr − 1 = m + n. We offer lower bounds for solutions of these boundary value problems in terms of sup0 t 1 |x(t)| and maxk∈{0,··· ,m+n} |y(k)|. These bounds further lead to inequalities for related Green’s functions which are very useful in the study of positive solutions of boundary value problems. Mathematics subject classification (1991): 34A40, 39A10.
16 citations
TL;DR: In this paper, the authors considered the boundary value problems with fixed signs and provided criteria for the existence of single and twin solutions of the system that are of fixed signs, respectively.
11 citations
TL;DR: In this paper, the existence of single-and double-fixed-sign solutions of the system is studied. But the authors do not consider the problem of single and double fixed sign solutions.
10 citations
TL;DR: In this paper, the existence of single and double solutions for the system with T = u1u2, u1cu2,u2cu 2,cu 3,cu 4,cu 5,cu 6,cu 7,cu 8,cu 9,cu 10,cu 11,cu 12,cu 13,cu 14,cu 15,cu 16,cu 17,cu 18,cu 19,cu 20,cu 21,cu 22,cu 23,cu 24,cu 25,cu 26,cu 27,cu 28,cu 29,cu 30
Abstract: We consider the following system where T≥1 and for each 1 ≤ i ≤ n, αi > 0, γi > o, βi ≥ 0, δi ≥ γi and αiγi(T+1)+αiδi+βiγi>0. Criteria are offered for the existence of single and double solutions u = u1u2,…,un) of the system such that each 1 ≤ i ≤ n, we have θ,ui ≥ 0 on {0,1,…,T+2} where θi≥ {1,-1}.
9 citations
9 citations
TL;DR: In this paper, the authors considered the boundary value problem with fixed signs and provided criteria for the existence of single and twin solutions of the problem. But they did not consider the problem of boundary value problems with fixed numbers.
Abstract: We consider the system of boundary value problems u (ni) i (t) + fi(t, u1(t), . . . , um(t)) = 0 u (j) i (0) = 0 u (pi) i (1) = 0 9 >= >; for t ∈ [0, 1], i = 1, . . . , m and 0 ≤ j ≤ ni−2 where ni ≥ 2 and 1 ≤ pi ≤ ni−1. Several criteria are offered for the existence of single and twin solutions of the system that are of fixed signs.
8 citations
TL;DR: In this paper, the authors considered the boundary value problem and developed criteria for @l to constitute an interval, bounded as well as unbounded, more so explicit intervals of @l are presented.
6 citations
TL;DR: In this paper, the boundary value problem is considered in the context of boundary value maximization, where Δ n y(k)=λP(k,y, Δ y, etc, Δ n−1 y), k=0,m, Δ j y(m i ) =0, j=0 and n i −1, where r⩾2, ni ⩾1 for i=1, r n i =n and 0=k1
TL;DR: In this paper, upper and lower solutions method is used to obtain the existence of a solution for the following system of boundary value problems: where ũi (k) = (ui, Δui (k), …, Δn-2 ui(k)), 1 ≤ i ≤ m.
Abstract: Abstract Upper and lower solutions method is used to obtain the existence of a solution for the following system of boundary value problems: where ũi (k) = (ui (k), Δui (k), … , Δn–2 ui (k)), 1 ≤ i ≤ m.
01 Feb 2000
TL;DR: In this article, the existence of positive solutions of the discrete focal boundary value problem was established, and positive solutions were found for the discrete FV problem with positive solutions for FV.
Abstract: In this chapter we shall establish the existence of positive solutions of the discrete focal boundary value problem
$${( - 1)^{n - p}}{\Delta ^n}y = \lambda P(k,y,\Delta y, \cdots ,{\Delta ^{n - 1}}y),k \in [0,T]$$
(20.1)
$${\Delta ^i}y(0) = 0,0ip - 1$$
(20.2)
$${\Delta ^i}y(T + 1) = 0,pin - 1.$$
(20.3)