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ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF FORCED NONLINEAR NEUTRAL DIFFERENCE EQUATIONS
Liu, Yuji,Ge, Weigao 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $\Delta[x(n)-\sumpi(n)x(n-k_i)]+\sumqj(n)f(x(n-\iota_j))=r(n)$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.
PERIODIC SOLUTIONS FOR A KIND OF p-LAPLACIAN HAMILTONIAN SYSTEMS
Li Zhang,Weigao Ge 대한수학회 2010 대한수학회보 Vol.47 No.2
In this paper, the existence of periodic solutions is obtained for a kind of p-Laplacian systems by the minimax methods in critical point theory. Moreover, the existence of infinite periodic solutions is also obtained.
Junfang Zhao,Weigao Ge 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, (∅p(x'(t)))' + h(t)f(t, x(t), |x'(t)|) = 0, 0 < t < 1, x'(0) −δx(η) = 0, x'(1) + δx(η) = 0, where ∅p(s) = |s|p−2s, p > 1, δ > 0, 1 > η > ξ > 0, ξ +η= 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interestingpoint is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now. In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, (∅p(x'(t)))' + h(t)f(t, x(t), |x'(t)|) = 0, 0 < t < 1, x'(0) −δx(η) = 0, x'(1) + δx(η) = 0, where ∅p(s) = |s|p−2s, p > 1, δ > 0, 1 > η > ξ > 0, ξ +η= 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interestingpoint is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.
Aijun Yang,Weigao Ge 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.2
This paper deals with the existence of positive solutions for a kind of multi-point nonlinear fractional differential boundary value problem at resonance. Our main approach is different from the ones existed and our main ingredient is the Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. And an example is constructed to show that our result here is valid.
Existence and uniqueness of positive solutions for singular three-point boundary value problems
Chunmei Miao,Weigao Ge 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
In this paper, the singular three-point boundary value problem u〃(t) + f(t,u) = 0, t 2 (0, 1), u(0) = 0, u(1) = αu(η), is studied, where 0 < η < 1, α > 0, f(t, u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results. In this paper, the singular three-point boundary value problem u〃(t) + f(t,u) = 0, t 2 (0, 1), u(0) = 0, u(1) = αu(η), is studied, where 0 < η < 1, α > 0, f(t, u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.
PERIODIC SOLUTIONS FOR A KIND OF p-LAPLACIAN HAMILTONIAN SYSTEMS
Zhang, Li,Ge, Weigao Korean Mathematical Society 2010 대한수학회보 Vol.47 No.2
In this paper, the existence of periodic solutions is obtained for a kind of p-Laplacian systems by the minimax methods in critical point theory. Moreover, the existence of infinite periodic solutions is also obtained.
Zhao, Junfang,Ge, Weigao The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.
Aijun Yang,Weigao Ge 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.4
In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x0(t))0 + f(t; x(t)) = 0; t 2 (0; 1); x0(0) = 0; x(1) = Z 1 0 x(s)g(s)ds: A new result on the existence of positive solutions is obtained. The interesting points are: the ¯rst, we employ a new tool{ the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.