无穷区间上二阶微分方程的边值问题

利用Schauder不动点定理讨论了一类非线性二阶微分方程在无穷区间上的边值问题无界解的存在性，部分改进了郭大钧教授最近得到的结果。     

Boundary Value Problems for Nonlinear Differential Equations of Second Order inBanach Spaces

ＢａｎａｃｈＳｐａｃｅｓＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓｏｆＳｅｃｏｎｄＯｒｄｅｒｉｎＢａｎａｃｈＳｐａｃｅｓＣｕｉＣｈａｎｇｊｕｎＬｉｕＹａｎｓｈｅｎｇ（Ｄｅｐｔ．ｏｆＭａ...     

奇异半正边值问题正解的存在性

过构造特殊的锥, 利用有界正线性算子的谱理论及不动点指数理论, 研究了奇异半正边值问题正解的存在性, 改进和推广了有关文献中的结果     

奇异半线性反应扩散方程初值问题的一些注记

考虑下述奇异半线性反应扩散方程初值问题(()-1-t△u=ut+f(x),t＞0,x∈RN lim u(t,x)=0,x∈RN t→0=)其中r＞0,△=∑( )/( )x2i,f(x)非负且f(x)∈L∞(RN).首先利用增算子不动点定理,重新证明了IVP在(0,+∞)上至少存在一个非负解,并给出了IVP解的迭代逼近序列.其次获得了一个有关IVP(1)正解的无限增长性的结果.最后,证明了当r＞1时,去掉条件1/r-1≥n/2,IVP的正解u(t)同样会产生爆破.研究结果表明情形limut→+∞(t,x)=+∞不会出现.     

Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin R~n

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅｓｅｍｉｌｉｎｅａｒｅｌｌｉｐｔｉｃｅｑｕａｔｉｏｎｓ△ｕ＋ｆ（ｕ）＝０（１．１）ｕ（ｘ）→０ａｓ｜ｘ｜→∞（１．２）ｉｎＲｎｗｅｒｅｃｏｎｓｉｄｅｒｅｄｗｉｄｅｌｙ（ｓｅｅ［１］－［７］）．Ｉｎｔｈｅｎｉｃｅｐａｐｅｒｓ［１］ａｎｄ［２］，ｉｔｗａｓｐｒｏｖｅｄｔｈａｔａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｏｆ（１．１）ｍｕｓｔｂｅｒａｄｉａｌｉｎｃａｓｅｆ（ｕ）∈Ｃ１＋δ（δ＞０）．Ｔｈｅｒｅｆｏｒｅ，ａｎｙｐｏｓｉｔｉｖｅｓｏｌｕｔｉ…     

次线性条件下奇异三阶微分方程周期边值问题解的全局结构

讨论三阶微分方程周期边值问题解的全局结构,其中ρ∈(0,1/3~(1/2))为常数,λ∈R~+=[0,+∞)为参数,f在t=0,t=2π和u=0处有奇异性,关于u处满足次线性增长条件。     

BOUNDEDNESS,ASYMPTOTIC BEHAVIOR AND OSCILLATORY PROPERTIES FOR THE MODELS OF SINGLE-SPECIES POPULATION GROWTH WITH IMPULSIVE EFFECT

1. IntroductionThe models of single-species population growth can be described as the following ordinary differelltial equations(IVP) X' ~ f(x,K(t)), x(to) = xo 2 0, (1.1)where K(t) > 0 is the carrying capacity of the environment. Much has been done underthe assumption that K(t) is either constant or changed periodicallyll-3]. However, onemay easily visualize in nature where abruput changes such as harvesting, and disajsters mayoccur. Consequently, we consider such model with impulses. It …     

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

This paper deals with the singular nonlinear third-order periodic boundary value problem u‘‘‘ ρ^3u = f(t,u), 0 ≤ t ≤ 2π, with u^(i)(0) = u^(i)(2π), i = 0,1,2, where ρ ∈ (0, 1 /√3) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2π] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.     

THE PERIODIC BOUNDARY PROBLE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH VARIABLE TIME

1 IntroductionIt is well known that the monotonic iterative technique is a successfulmethod to obtain the extremal solutions of ODE or IDE with fixed time (see[IJ, [2]). Some results about the monotonic iterative technique for IDE withvariable time were obtained in the past few years (see [3--7]). Because thetheory of IDE with variable time is more complicated than that of IDE withfixed time, many authors considered the special case in which the pulse surfacet = T(x) is strictly monoton…