A singular nonlinear boundary-value problem

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 $pgeq 0$, $lambda$ is a positive constant, and $phi$ is a positive function in $L^1_{{m loc}}(0,1)$. Moreover, we derive asymptotic estimates describing the behavior of the solution and its derivative at the boundary.

Keywords

• Singular nonlinear boundary value problems
• existence and uniqueness
• asymptotic estimates.