Electron. J. Diff. Equ., Vol. 2010(2010), No. 22, pp. 1-20.

Monotone positive solutions for p-Laplacian equations with sign changing coefficients and multi-point boundary conditions

Jianye Xia, Yuji Liu

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 4, 2010.
Math Subject Classifications: 34B10, 34B15, 35B10.
Key Words: Second order differential equation; positive solution multi-point boundary value problem.

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Jianye Xia
Department of Mathematics
Guangdong University of Finance
Guangzhou 510320, China
email: JianyeXia@sohu.com
Yuji Liu
Department of Mathematics
Hunan Institute of Science and Technology
Yueyang 414000, China
email: liuyuji888@sohu.com

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