Existence Results for Singular Anisotropic Elliptic Boundary-value Problems
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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
uαuxx + ubuyy + 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.
CitationKim, E. H. (2000). Existence results for singular anisotropic elliptic boundary-value problems. Electronic Journal of Differential Equations, 2000(17), pp. 1-17.
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