一类拟线性微分方程组边值问题的3个正解  

Three positive solutions to boundary value problems for a class of quasilinear differential equation systems

作　　者：郭彦平[1] 邢化明[2] 

机构地区：[1]河北科技大学理学院,河北石家庄050018 [2]廊坊师范学院数学系,河北廊坊065000

出　　处：《河北科技大学学报》2005年第1期10-14,24,共6页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金资助项目(10371030);河北省自然科学基金资助项目(603384)

摘　　要：针对在分析非线性现象时,得到的许多数学模型仅仅是对正解有意义的问题,讨论二阶拟线性微分方程组(φｐ(ｘ′))′+ａ(ｔ)ｆ(ｔ,ｘ,ｙ)=0,(φｑ(ｙ′))′+ｂ(ｔ)ｇ(ｔ,ｘ,ｙ)=0在非线性边值条件ｘ(0)-Ｂ0(ｘ′(0))=0,ｘ′(1)=0,ｙ(0)-Ｂ1(ｙ′(0))=0,ｙ′(1)=0及ｘ′(0)=0,ｘ(1)+Ｂ0(ｘ′(1))=0,ｙ′(0)=0,ｙ(1)+Ｂ1(ｙ′(1))=0下的边值问题,其中ｆ,ｇ是非负连续的函数。利用5个泛函的不动点定理,并且赋予ｆ和ｇ一些增长条件得到至少存在3个正确的判据。In analyzing nonlinear phenomena many mathematical models given are problems to which only positive solutions make sense.In this paper,we study boundary value problem for the second order quasilinear differential equation system ((φ_p(x′))′+)a(t)f(t,x,y)=0,(φ_q(y′))′+b(t)g(t,x,y)=0 subject to the following nonlinear boundary conditions x(0)-(B_0(x′(0)))=0,x′(1)=0,y(0)-B_1(y′(0))=0,y′(1)=0 and x′(0)=0,x(1)+B_0(x′(1))=0,y′(0)=0,y(1)+B_1(y′(1))=0 respectively,where f,g are continuous and nonnegative functions.Using the five functionals fixed point theorem and imposing some growth conditions on f and g yield existence criteria of at least three positive solutions.

关 键 词：拟线性 微分方程组 边值问题 正解 非线性边值条件 泛函 不动点定理 判据 非线性现象 

分 类 号：O175[理学—数学] O174[理学—基础数学]