Existence and uniqueness of positive solutions for singular nonlinear elliptic boundary value problems. (English) Zbl 1155.35375
Summary: We establish the existence and the uniqueness of positive solutions for Dirichlet boundary value problems of nonlinear elliptic equations with singularity. We obtain the existence and the uniqueness by using the mixed monotone method in the cone theory. Moreover, we give an iterative method of constructing the solution. The rate of convergence of the iterative sequence is analyzed.
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35J60 | Nonlinear elliptic equations |
| 35A35 | Theoretical approximation in context of PDEs |
Keywords:
existence; uniqueness; singularity; positive solution; mixed monotone operator; Dirichlet boundary value problems; iterative methodReferences:
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