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Existence and Multiplicity of Positive Solutions for Singular Semipositone p-Laplacian Equations
Published online by Cambridge University Press: 20 November 2018
Abstract
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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.
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- Copyright © Canadian Mathematical Society 2006
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