Existence and Multiplicity of Positive Solutions for Singular Semipositone $p$-Laplacian Equations

http://dx.doi.org/10.4153/CJM-2006-019-2
Canad. J. Math. 58(2006), 449-475

  Published:2006-06-01
 Printed: Jun 2006

Positive solutions are obtained for the boundary value problem \[\begin{cases} -( | u'| ^{p-2}u')' =\lambda f( t,u),\;t\in ( 0,1) ,p>1\\ u( 0) =u(1) =0. \end{cases} \] Here $f(t,u) \geq -M,$ ($M$ is a positive constant) for $(t,u) \in [0\mathinner{,}1] \times (0,\infty )$. We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.