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

This article concerns the existence, multiplicity of positive solutions for the integral boundary-value problem with $phi$-Laplacian, $$displaylines{ ig(phi(u'(t))ig)'+f(t,u(t),u'(t))=0,quad tin[0,1],cr u(0)=int_0^1 u(r)g(r),dr,quad u(1)=int_0^1u(r)h(r),dr, }$$ 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.