Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 219, pp. 1-9.
Title: Monotone iterative method for obtaining positive solutions
of integral boundary-value problems with phi-Laplacian operator
Author: Yonghong Ding (Tianshui Normal Univ., China)
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.