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# Existence results for singular anisotropic elliptic boundary-value problems ∗

@inproceedings{KimExistenceRF, title={Existence results for singular anisotropic elliptic boundary-value problems ∗}, author={Eun Heui Kim} }

We establish the existence of a positive solution for anisotropic singular quasilinear elliptic boundary-value problems. As an example of the problems studied we have uuxx + u uyy + λ(u+ 1) a+r = 0 with zero Dirichlet boundary condition, on a bounded convex domain in R . Here 0 ≤ b ≤ a, and λ, r are positive constants. When 0 < r < 1 (sublinear case), for each positive λ there exists a positive solution. On the other hand when r > 1 (superlinear case), there exists a positive constant λ such… CONTINUE READING