Multiple positive solutions for some p-Laplacian boundary value problems

作者：Ji Dehong^*; Ge Weigao

来源：Applied Mathematics and Computation, 2007, 187(2): 1315-1325.

DOI：10.1016/j.amc.2006.09.041

• triple positive solutions
• p-Laplacian
• boundary value problems
• fixed point theorem
• cone

This paper deals with the existence of multiple positive solutions for the one-dimensional p-Laplacian
(phi(p)(x(1)(t)))(1) + q(t)f(t,x(t),x(1)(t)) = 0, t is an element of (0, 1)
subject to the following boundary value conditions:
x(0) = (n)Sigma(i=1)alpha(i)x(xi(i)), x(1) = (n)Sigma(i=1)beta(i)x(xi(i)),
where phi(p)(s) = vertical bar s vertical bar(p-2) .s, p > 1. By means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem.

• 出版日期2007-4-15
• 单位北京理工大学