一维p-Laplacian方程多点边值问题迭代解的存在性

Existence and Iteration of Solutions for a Multi-point Boundary Value Problem with a p-Laplacian Operator

运用Mawhin定理、上下解方法以及单调迭代技巧得到了下列具有p-Laplacian算子的多点边值问题{(φ_p(u′))′+f(t,u)=0,0≤t≤1,u(0)=0,u(1)=∑_(i=1)^(m-2)γ_iu(η_i)迭代解的存在性.进一步地,在允许f(t,u)变号的前提下,我们给出充分条件以保证解的非负性和非正性.

By employing Mawhin＇s continuation theorem, we obtain the existence of solutions and establish a corresponding iterative scheme for BVP, {（φp（u′））′＋f（t,u）=0,0≤t≤1, u（0）=0,u（1）=∑（i=1）^（m-2）γiu（ηi） The upper and lower solutions method and monotone iterative technique are used. Furthermore, we impose sufficient conditions on f（t, u） which can guarantee the existence of nonnegative or nonpositive solutions even when f（t, u） is allowed to change sign.