Geodesic
Existence and Multiplicity of Positive Solutions for Singular Semipositone p-Laplacian Equations
Canadian journal of mathematics, Tome 58 (2006) no. 3, pp. 449-475

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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.
DOI : 10.4153/CJM-2006-019-2
Mots-clés : 34B15, one dimensional, p-Laplacian, positive solution, degree theory, upper and lower solution 
Agarwal, Ravi P.; Cao, Daomin; Lü, Haishen; O'Regan, Donal. Existence and Multiplicity of Positive Solutions for Singular Semipositone p-Laplacian Equations. Canadian journal of mathematics, Tome 58 (2006) no. 3, pp. 449-475. doi: 10.4153/CJM-2006-019-2
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