Electron. J. Diff. Eqns., Vol. 2005(2005), No. 86, pp. 1-9.

Positive solutions and eigenvalues of nonlocal boundary-value problems

Jifeng Chu, Zhongcheng Zhou

We study the ordinary differential equation $x''+\lambda a(t)f(x)=0$ with the boundary conditions $x(0)=0$ and $x'(1)=\int_{\eta}^{1}x'(s)dg(s)$. We characterize values of $\lambda$ for which boundary-value problem has a positive solution. Also we find appropriate intervals for $\lambda$ so that there are two positive solutions.

Submitted April 18, 2005. Published July 27, 2005.
Math Subject Classifications: 34B15
Key Words: Nonlocal boundary-value problems; Positive solutions; eigenvalues; fixed point theorem in cones.

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Jifeng Chu
Department of Applied Mathematics
College of Sciences, Hohai University
Nanjing 210098, China
email: jifengchu@hhu.edu.cn
Zhongcheng Zhou
School of Mathematics and Finance
Southwest Normal University
Chongqing 400715, China
email: zhouzc@swnu.edu.cn

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