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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 \[ \begin{cases} x''+\Phi(t)f(t,x(t),x'(t))=0,\quad 0<t<1, \\ x(0)=x(1)=0\end{cases} \] is presented by using the fixed point index; here \(f\) may be singular at \(x = 0\).

MSC:

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