u" + a(t)f(u) = o, u(0) = 0, u(1) au(~) = b, where b, c~ > 0, r/ E (0, 1), a~? < 1, are given. Under su i tab le condi t ions , we show t h a t the re exis ts a posi t ive n u m b e r b* such t h a t… (More)

Ruyun Ma, Tianlan Chen, and Yanqiong Lu Department of Mathematics, Northwest Normal University, Lanzhou 730070, China Correspondence should be addressed to Ruyun Ma, ruyun ma@126.com Received 12… (More)

is a forward difference operator with uk = u(tk), uk = u(tk+) – u(tk), tN = T and ∇ is a backward difference operator with ∇uk = u(tk) – u(tk–), t = , f : [, T] ×R → R is continuous. In… (More)

We consider the fourth-order boundary value problem u0000 1⁄4 f ðt,u,u00Þ, 0 < t < 1 uð0Þ 1⁄4 uð1Þ 1⁄4 u00ð0Þ 1⁄4 u00ð1Þ 1⁄4 0 where f(t,u,p) = au b p + (j(u,p)j) near (0,0), and f(t,u,p) = cu dp +… (More)