We establish the existence of a positive solution of a class of anisotropic singular quasilinear elliptic boundary value problems with certain nonlinearities. One example is: [Special characters omitted.] Here Ω is a bounded convex smooth domain in R 2 , a ≥ b ≥ 0, λ > 0, and r > 0.
If 0 < r < 1 (sublinear case), then (1) has a solution for all λ > 0. On the other hand, if r > 1 (superlinear case), then there exists a positive constant λ* such that for each λ ∈ (0, λ*], (1) has a positive solution.
Finally, we present some numerical results for some open theoretical questions for these types of problems.
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