EXISTENCE OF POSITIVE SYMMETRIC SOLUTIONS FOR AN INTEGRAL BOUNDARY-VALUE PROBLEM WITH phi-LAPLACIAN OPERATOR

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