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

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.

Keywords

• phi-Laplacian
• fixed point
• cone
• positive symmetric solutions