时标上三阶非线性ρ-Laplacian三点边值问题的正解

摘要

The following third order nonlinear p- Laplacian three-point boundary value problems on time SCales [φp(p(t)u△▽(t))]▽ +a(t)f(t,u(t)) =0, t ∈ [0,T],βu(0) -γu△(0) = 0,u△(T)=αu(η),u△▽(0)=0are studied. By means of five functionals fixed point theorems in cones, some new results for the existence of at least three positive solutions of the boundary value problem are obtained. As an application, an example is given to illustrate the main result.%研究了时标上三阶非线性ρ-Laplacian三点边值问题[φp(p(t)u△▽(t))]▽+a(t)f(t,u(t))=0,t∈[O,T],βu(0)-γu△(0)=0,u△(T)=αu(η),u△▽(0)=0借助于锥上的五泛函不动点定理,得到了边值问题至少有三个正解的一些新的结果,同时给出了例子验证了主要结果.