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Existence and Multiplicity of Positive Solutions for Singular Semipositone p-Laplacian Equations
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- Journal:
- Canadian Journal of Mathematics / Volume 58 / Issue 3 / 01 June 2006
- Published online by Cambridge University Press:
- 20 November 2018, pp. 449-475
- Print publication:
- 01 June 2006
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- Article
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Positive solutions are obtained for the boundary value problem
$$\left\{ _{u\left( 0 \right)\,=\,u\left( 1 \right)\,=\,0}^{-{{\left( {{\left| {{u}'} \right|}^{p-2}}{u}' \right)}^{\prime }}\,=\,\lambda f\left( t,\,u \right),\,t\,\in \,\left( 0,\,1 \right),\,p\,>\,1} \right.$$Here
$f(t,u)\ge -M$, (
$M$ is a positive constant) for $(t,u)\in [0,1]\times (0,\infty )$. We will show the existence of two positive solutions by using degree theory together with the upper–lower solution method.
