一类非线性项包含导数的边值问题伪对称解的存在性

Existence of Pseudo-symmetric Solutions to A p-Laplacian Boundary Value Problem with Nonlinear Term Involving Derivative on Time Scale

研究时标上非线性项包含低阶导数的p-Laplacian三点边值问题：（φ_p（u~Δ（t）））~v＋h（t）f（t,u（t）,u~Δ（t））=0,t∈（0,T）T,u（0）=0,u（η）=u（T）伪对称解的存在性,其中η∈（0,T）T且T在[η,T]T上是对称的,p〉1,φp（u）=up-2u.利用伪对称技巧和锥上的五泛函不动点定理证明了边值问题至少有3个正的伪对称解.作为应用,给出例子验证了所得结果.所得结论在相应的微分方程（T=R）,差分方程（T=Z）以及通常的时标上都是新的.

The following three-point boundary value problem for p-Laplacian dynamic equations with nonlinear term involving derivative on time scales T of the form is considered（φ_p（u~Δ（t）））~v＋h（t）f（t,u（t）,u~Δ（t））=0,t∈（0,T）_T,u（0）=0,u（η）=u（t）,where pη∈（0,T）T,T is symmetric in[η,T]T and φp（u）= u-2u with p〉1.By using pseudo-symmetric technique and the five functional fixed-point theorem,it is proved that the boundary value problem has at least three positive pseudo-symmetric solutions under some assumptions.As an application,an example is given to illustrate the main results.The results are new even for the corresponding differential（T=R）,difference equations（T=Z）as well as in general time scales.