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.