Electron. J. Diff. Equ., Vol. 2012 (2012), No. 219, pp. 1-9.

Monotone iterative method for obtaining positive solutions of integral boundary-value problems with phi-Laplacian operator

Yonghong Ding

Abstract:
This article concerns the existence, multiplicity of positive solutions for the integral boundary-value problem with $\phi$-Laplacian,
$$\displaylines{ \big(\phi(u'(t))\big)'+f(t,u(t),u'(t))=0,\quad t\in[0,1],\cr u(0)=\int_0^1 u(r)g(r)\,dr,\quad u(1)=\int_0^1u(r)h(r)\,dr, }$$
where $\phi$ is an odd, increasing homeomorphism from R to R. Using a monotone iterative technique, we obtain the existence of positive solutions for this problem, and present iterative schemes for approximating the solutions.

Submitted October 11, 2012. Published November 29, 2012.
Math Subject Classifications: 34B15, 34B18.
Key Words: phi-Laplacian; monotone iterative; cone; positive solutions.

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Yonghong Ding
Department of Mathematics
Tianshui Normal University
Tianshui 741000, China
email: dyh198510@126.com

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