非齐次边值条件下一类静态梁方程的正解  

Positive solutions to an equation of elastic beams simply supported at both ends with derivative terms

作　　者：宋灵宇[1] 

机构地区：[1]长安大学,陕西西安710064

出　　处：《甘肃工业大学学报》2002年第2期114-116,共3页Journal of Gansu University of Technology

摘　　要：讨论带导数项的方程 y( 4) (x) =f(x ,y(x) ,y′(x) ,y″(x) ,y (x) )在非齐次边值条件 y(0 )=a ,y(1) =b ,y″(0 ) =c ,y″(1) =d下正解的存在性 ,其中a≥ 0 ,b≥ 0 ,c≤ 0 ,d≤ 0 .假定 f在零点次线性增长 ,在无穷远点超线性增长 ,则上述问题当max{a ,b ,-c ,-d}充分小时有非负解存在 ,当max{a ,b ,-c ,-d}充分大时无非负解存在 .The existence of positive solutions to an e qu ation with derivative terms y (4)(x)=f(x,y(x), y′(x),y″(x),y(x)) under non homogeneous boundary value conditions y(0)=a,y(1)=b,y″(0)=c, y ″(1)=d, where a≥0,b≥0,c≤0,d≤0, is discussed. Assuming f to be s ub linearly increasing at the point of zero and super linearly increasing at inf inity, then there would be nonnegative solutions for above mentioned problem wh en max{a,b,-c,-d} was sufficiently small or no nonnegative solutions when max{a,b,-c, -d} was sufficiently large.

关 键 词：非齐次边值条件 静态梁方程 四阶边值问题 导数项 正解 存在性 

分 类 号：O175.15[理学—数学] O175.8[理学—基础数学]