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Singular mixed boundary value problem. (English) Zbl 1103.34009

A singular nonlinear boundary value problem is studied in the form \[ u''+f(t,u, u')=0, \quad u'(0)=0,\quad u(T)=0. \] The nonnegative nonlinearity \(f\) is defined on \((0,T)\times(0,\infty)\times x(-\infty,0)\) and can have singularities. Sufficient conditions are given for the existence of a positive solution. The considerations are based on the technique of lower and upper functions. An illustrative example is given.

MSC:

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