具p-Laplacian算子的四阶三点边值问题的迭代解

The Iterative Solutions to Fourth-order Three-point Boundary Value Problems with p-Laplacian

研究下列具有p-Laplacian算子的四阶三点边值问题(φp(u″(t)))″=f(t,u(t),u″(t)),t∈[0,1]u(0)-ξu(1)=0,u′(1)-ηu′(0)=0,u″(0)-au″(δ)=0,u″(1)-bu″(δ)=0,其中φp(s)=sp-2s,p>1,0<ξ,η<1,0<a,b<1,0<δ<1,f∈C([0,1]×R2,R),通过单调迭代方法得到迭代解。

The fourth-order three-point boundary value problems with p-Laplacian {（φp（u″（t）））″=f（t,u（t）,u″（t））,t∈[0,1]u（0）-ζu（1）=0,u′（1）-ηu′（0）=0,u″（0）-au″（δ）=0,u″（1）-bu″（δ）=0,is studied, where φp（s）=｜s｜p-2s,p〉1,0〈ζ,η〈1,0〈a,b〈1,0〈δ〈1,f∈C（[0,1]×R2,R）.The existence of iterative solutions is obtained by monotone iterative technique.