Positive solutions of singular Dirichlet boundary value problems with time and space singularities. (English) Zbl 1192.34027

The author studies the existence of positive solutions of a Dirichlet boundary value problem. The nonlinearity \(h(t,x,y)\) involved in the differential equation can be singular in the time variable \(t\), at \(t=0\) and/or \(t=T\), and can have a weak or strong singularity in the space variable, at \(x=0\). The approach relies on regularization and sequential techniques combined with the method of lower and upper functions. The author also investigates the existence of a maximal positive solution for this boundary value problem. Some examples are given to illustrate the theory.


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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