Kim, Eun Heui2019-12-182019-12-182000-02-29Kim, E. H. (2000). Existence results for singular anisotropic elliptic boundary-value problems. <i>Electronic Journal of Differential Equations, 2000</i>(17), pp. 1-17.1072-6691https://hdl.handle.net/10877/9117We establish the existence of a positive solution for anisotropic singular quasilinear elliptic boundary-value problems. As an example of the problems studied we have uα uxx+ ub uyy + λ (u + 1)α+r = 0 with zero Dirichlet boundary condition, on a bounded convex domain in ℝ2. Here 0 ≤ b ≤ α, 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 that for λ in (0, λ*) there exists a positive solution, and for λ* < λ there is no positive solution.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalAnisotropicSingularSublinearSuperlinearElliptic boundary-value problemsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.