Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 22, pp. 1-20.

Title: Monotone positive solutions for p-Laplacian equations with
       sign changing coefficients and multi-point boundary conditions
       
Authors: Jianye Xia (Guangdong Univ. of Finance, Guangzhou, China)
         Yuji Liu (Hunan Inst of Science and Tech., Yueyang, China) 

Abstract: 
 We prove the existence of three monotone positive solutions
 for the second-order multi-point boundary value problem,
 with sign changing coefficients,
 $$\displaylines{
 [p(t)\phi(x'(t))]'+f(t,x(t),x'(t))=0,\quad t\in (0,1),\cr
  x'(0)=-\sum_{i=1}^la _ix'(\xi_i)+\sum_{i=l+1}^ma_ix'(\xi_i),\cr
 x(1)+\beta x'(1)=\sum_{i=1}^kb_ix(\xi_i)-\sum_{i=k+1}^mb_ix(\xi_i)
 -\sum_{i=1}^mc_ix'(\xi_i).
 }$$
 To obtain these results, we use a fixed point theorem  for
 cones in Banach spaces. Also we present an example that illustrates
 the main results.
	 
Submitted October 26, 2009. Published February 04, 2010.
Math Subject Classifications: 34B10, 34B15, 35B10.
Key Words: Second order differential equation; positive solution
           multi-point boundary value problem.