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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.

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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