Showing papers by "Patricia J. Y. Wong published in 2007"
22 citations
TL;DR: In this paper, the authors investigated a second-order nonlinear difference equation with sign-changing nonlinearity subject to two different sets of nonlocal boundary conditions and established sufficient conditions for the existence of multiple positive solutions of the boundary value problem.
22 citations
TL;DR: Criteria are offered for the existence of one and more constant-sign solutions u of the system in (C[0,T])^n and some of its particular cases that arise from physical problems.
Abstract: We consider the following system of Volterra integral equations: u"i(t)=@!"0^tg"i(t,s)[f"i(s,u"1(s),u"2(s),...,u"n(s))+h"i(s,u"1(s),u"2(s),...,u"n(s))]ds,t@?[0,T],1@?i@?n and some of its particular cases that arise from physical problems. Criteria are offered for the existence of one and more constant-sign solutions u=(u"1,u"2,...,u"n) of the system in (C[0,T])^n. We say u is of constant sign if for each 1@?i@?n,@q"iu"i(t)>=0 for all t@?[0,T], where @q"i@?{1,-1} is fixed. Examples are also included to illustrate the results obtained.
9 citations
TL;DR: In this article, the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions is studied. But the authors focus on the case of BVPs without growth restrictions.
Abstract: Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein–Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.
8 citations
TL;DR: In this paper, the authors considered a model that describes the dynamics of epidemics in homogeneous/heterogeneous populations as well as the spreading of multiple inter-related infectious diseases.
Abstract: We consider the following model that describes the dynamics of epidemics in homogeneous/heterogeneous populations as well as the spreading of multiple inter-related infectious diseases: u i ( k ) = ∑ l = k - τ i k - 1 g i ( k , l ) f i ( l , u 1 ( l ) , u 2 ( l ) , … , u n ( l ) ) , k ∈ Z , 1 ⩽ i ⩽ n . Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic solutions ( u 1 , u 2 , … , u n ) , i.e., for each 1 ⩽ i ⩽ n , u i is periodic and θ i u i ⩾ 0 where θ i ∈ { 1 ,- 1 } is fixed. Examples are also included to illustrate the results obtained.
5 citations
DOI•
01 Sep 2007
TL;DR: In this article, the authors considered a generalized right focal boundary value problem and established the existence of fixed point theorems for one or more fixed-sign solutions, i.e., for each 1, 2, · · ·, $n, $1/2 (a + b) 0, and the deviating arguments are fixed.
Abstract: We consider the following system of third-order three-point generalized right focal boundary value problems
$u^(''')_ i (t) = f_i(t, u_1(\phi_ 1(t)), u_2(\phi_ 2(t)), · · · , u_n(\phi_ n(t))), t \in [a, b]$
$u_i(a) = u^'_i(z_i) = 0$, \gamma_i u_i(b) + \delta_iu^('')_i (b) = 0$
where $i$ = 1, 2, · · · , $n$, $1/2 (a + b) 0$, and $\phi_ i$ are deviating arguments. By using some fixed point theorems, we establish the existence of one or more fixed-sign solutions $u = (u_1, u_2, · · · , u_n)$ for the system, i.e., for each 1 $ = 0$ for $t \in [a, b]$, where $\theta_i \in$ {1,−1} is fixed. An example is also presented to illustrate the results obtained.
4 citations
TL;DR: In this article, a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and also in the dependent arguments is considered, and the Schauder fixed point theorem is used to establish criteria such that the problem has at least one fixed-sign solution.
4 citations
TL;DR: In this article, the authors considered the boundary value problem with conjugate boundary conditions and established criteria for the existence of three positive solutions of the problem using different fixed point theorems.
Abstract: We consider the following differential equation on a time scale T
yΔΔ(t) + P(t, y(σ(t))) = 0, t ∈ [a, b] ∩ T
subject to conjugate boundary conditions
y(a) = 0, y(σ2(b)) = 0
where a, b ∈ T and a < σ(b). By using different fixed point theorems, criteria
are established for the existence of three positive solutions of the boundary
value problem. Examples are also included to illustrate the results obtained.
3 citations
01 Jan 2007
TL;DR: In this paper, the oscillatory properties of the equations d2 dt2 ( 1 a(t) ( dx(t))α + q(tf (x[g(t])]) = 0 and d2dt2( 1 a (t)(dx(t )α) = q(T)f(x [g (t])+ p(t]h(x[σ(t)]), where α is the ratio of two positive odd integers.
Abstract: In this paper we shall investigate the oscillatory properties of the equations d2 dt2 ( 1 a(t) ( dx(t) dt )α) + q(t)f (x[g(t)]) = 0 and d2 dt2 ( 1 a(t) ( dx(t) dt )α) = q(t)f (x[g(t)])+ p(t)h(x[σ(t)]), where α is the ratio of two positive odd integers. AMS subject classification: 34C10.
3 citations