Electron. J. Diff. Equ., Vol. 2015 (2015), No. 295, pp. 1-7.

Existence and asymptotic behavior of positive solutions for a second-order boundary-value problem

Ramzi S. Alsaedi

Abstract:
We study the boundary-value problem
$$\displaylines{ \frac{1}{A(t)}(A(t)u'(t))'=\lambda f(t,u(t))\quad t\in (0,\infty),\cr \lim_{t\to 0^+}A(t)u'(t)=-a\leq 0, \quad \lim_{t\to \infty}u(t)=b>0, }$$
where $\lambda\geq0$ and f is nonnegative continuous and non-decreasing with respect to the second variable. Under some assumptions on the nonlinearity f, we prove the existence of a positive solution for $\lambda$ sufficiently small. Our approach is based on the Schauder fixed point theorem.

Submitted September 20, 2015. Published November 30, 2015.
Math Subject Classifications: 34B09, 34B15, 34B18, 34B27, 34B40.
Key Words: Boundary value problem; positive solution; fixed point; Green function.

Show me the PDF file (188 KB), TEX file, and other files for this article.

Ramzi S. Alsaedi
Department of Mathematics, Faculty of Sciences
King Abdulaziz University, P.O. Box 80203
Jeddah 21589, Saudi Arabia
email: ramzialsaedi@yahoo.co.uk

Return to the EJDE web page