## Unbounded positive solutions for second order singular boundary value problems with derivative dependence on infinite intervals.(English)Zbl 1158.34011

Summary: The existence of at least one unbounded positive solution and the existence of multiple unbounded positive solutions are established for the singular second-order boundary value problem
$p(t)^{-1}(p(t)x^\prime (t))^\prime +\varPhi(t)f(t,x,px^\prime)=0, 0<t<+\infty,$
$x(0)=0, \lim_{t\to+\infty}p(t)x^\prime (t)=0,$
using the fixed point index, where $$f$$ may be singular at $$px^\prime =0$$.

### MSC:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B40 Boundary value problems on infinite intervals for ordinary differential equations

### Keywords:

boundary value problems; singularity; fixed point index
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