## Positive solutions of singular second-order Neumann boundary value problem.(English)Zbl 1090.34524

Summary: Consider the following singular second-order Neumann boundary value problem $-u''(t)+a(t)u(t)=f\bigl(t,u(t)\bigr),\quad u'(0) =u'(1),$ where $$a:[0,1]\to(0,\infty)$$ and $$f:(0,1)\times[0, \infty)\to[0,\infty)$$ are continuous and $$f(t,u)$$ is singular at $$t=0,1$$. We obtain the existence of positive solutions by using the fixed-point indices; the result generalizes some present results.

### MSC:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations