Electron. J. Diff. Equ., Vol. 2009(2009), No. 159, pp. 1-7.

Existence of solutions for nonlinear second-order two-point boundary-value problems

Rui-Juan Du

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.

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Rui-Juan Du
Department of Computer Science, Gansu Political Science and Law Institute
Lanzhou, Gansu, 730070, China
email: drjlucky@163.com

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