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

Li, Zhilong

Ann. Differ. Equations 21, No. 3, 321-326 (2005).

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