基于非线性项变号的p-Laplacian方程两点边值问题正解的存在性

Existence of Positive Solutions for Two-point Boundary Value Problem with p-Laplacian Based on Nonlinear Sign-changing Terms

该文利用不动点指数理论,考虑了边值问题(BVP)(φ_p(u′(t)))′+a(t)f(t,u(t))=0,0<t<1,u′(0)=u(1)=0或u(0)=u(1)=0在非线性项f(t,u)可变号的情况下两个正解存在的充分条件,推广和改进了现有文献的结果.

This paper deals with the p-Laplacian equation （φp（u′（t）））′＋a（t）f（t,u（t））=0,0t1,u′（0）=u（1）=0 or u（0）=u（1）=0 whereφp（x） = ｜x｜^p-2x,p1.By using the fixed point index theory on cones,sufficient conditions for the existence of at least two positive solutions to the boundary value problem mentioned above are established.The known results are generalized and improved.