Electron. J. Differential Equations, Vol. 2016 (2016), No. 336, pp. 1-9.

Existence of positive symmetric solutions for an integral boundary-value problem with phi-Laplacian operator

Yonghong Ding

Abstract:
In this article, we show the existence of three positive symmetric solutions for the integral boundary-value problem with $\phi$-Laplacian
$$\displaylines{ (\phi(u'(t)))'+f(t,u(t),u'(t))=0,\quad t\in[0,1],\cr u(0)=u(1)=\int_0^1u(r)g(r)\,dr, }$$
where $\phi$ is an odd, increasing homeomorphism from $\mathbb{R}$ onto $\mathbb{R}$. Our main tool is a fixed point theorem due to Avery and Peterson. An example shows an applications of the obtained results.

Submitted May 18, 2016. Published December 28, 2016.
Math Subject Classifications: 34B15, 34B18.
Key Words: phi-Laplacian; fixed point; cone; positive symmetric solutions.

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

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