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

We study the boundary-value problem
 \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.

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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

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