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Multiple positive solutions of singular Dirichlet second-order boundary-value problems with derivative dependence. (English) Zbl 1203.34036

Summary: The existence of multiple positive solutions for the singular Dirichlet boundary-value problem

$\left\{\begin{array}{c}{x}^{\text{'}\text{'}}+{\Phi }\left(t\right)f\left(t,x\left(t\right),{x}^{\text{'}}\left(t\right)\right)=0,\phantom{\rule{1.em}{0ex}}0

is presented by using the fixed point index; here $f$ may be singular at $x=0$.

##### MSC:
 34B16 Singular nonlinear boundary value problems for ODE 34B18 Positive solutions of nonlinear boundary value problems for ODE 47N20 Applications of operator theory to differential and integral equations
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