A class of 2nth-order singular boundary value problems

作者：Wei Zhongli^*; Pang Changci

来源：Nonlinear Analysis-Theory Methods & Applications, 2007, 66(6): 1225-1245.

DOI：10.1016/j.na.2006.01.014

• singular boundary value problem
• positive solution
• lower and upper solution
• maximum principle
• a partial ordering
• 2nth order

This paper investigates the existence of positive solutions for 2nth-order (n > 1) singular sub-linear boundary value problems. First of all, we establish the maximal principle and some important lemmas. Then, we define a partial ordering in C2n-2 [0, 1] boolean AND C-2n (0, 1) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C2n-2[0, 1] as well as C2n-1[0, 1] positive solutions. Our nonlinearity f (t, x(1), x(2),...,x(n)) may be singular at x(i) = 0, i = 1, 2,...,n, t = 0 and/or t = 1.

• 出版日期2007-3-15
• 单位山东大学