Fourth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 03, 1999, pp. 75-90.

A singular nonlinear boundary-value problem

Robert M. Houck & Stephen B. Robinson

Abstract:
In this paper we prove an existence and uniqueness theorem for the singular nonlinear boundary-value problem
$$\displaylines{ (|y'(t)|^py'(t))'+\frac{\phi}{y^{\lambda}(t)}=0 \hbox{ in } (0,1),\cr y(0)=0=y(1), }$$
where $p\geq 0$, $\lambda$ is a positive constant, and $\phi$ is a positive function in $L^1_{{\rm loc}}(0,1)$. Moreover, we derive asymptotic estimates describing the behavior of the solution and its derivative at the boundary.

Published July 10, 2000.
Math Subject Classifications: 34B15.
Key Words: Singular nonlinear boundary value problems, existence and uniqueness, asymptotic estimates.

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Robert M. Houck
Department of Mathematics and Computer Science
Wake Forest University
Winston-Salem, NC 27109, USA
e-mail: houck@mthcsc.wfu.edu

Stephen B. Robinson
Department of Mathematics and Computer Science
Wake Forest University
Winston-Salem, NC 27109, USA
e-mail: robinson@mthcsc.wfu.edu

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