Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 159, pp. 1-7.
Title: Existence of solutions for nonlinear second-order
two-point boundary-value problems
Author: Rui-Juan Du (Gansu Political Science and Law Inst., China)
Abstract:
We consider the existence of solutions for the nonlinear
second-order two-point ordinary differential equations
$$\displaylines{
u''(t)+\lambda u(t)+g(u(t))=h(t),\quad t\in[0,1] \cr
u(0)=u(1)=0, \quad\hbox{or} \quad
u'(0)=u'(1)=0
}$$
where $g:\mathbb{R}\to \mathbb{R}$ is continuous, and
$h\in L^1(0,1)$.
Submitted May 25, 2009. Published December 15, 2009.
Math Subject Classifications: 34B15.
Key Words: Two-point boundary value problem;
existence; Leray-Schauder theory.