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Positive radial solution of a class of nonlinear Dirichlet boundary value problems. (Chinese. English summary) Zbl 1199.35115

Summary: By constructing a suitable cone and applying the fixed point theorem of cone expansion and compression type, the existence of a positive radial solution is studied for a class of singular elliptic Dirichlet boundary value problems, where the nonlinear term may be singular. Main results show that the existence of positive radial solution depends only upon the properties of the nonlinear term on a bounded subset of its domain, and the existence is independent of the properties of nonlinear term outside this set.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B09 Boundary eigenvalue problems for ordinary differential equations
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