论文信息 - Classical and Weak Solutions of a Singular Semilinear Elliptic Problem

Classical and Weak Solutions of a Singular Semilinear Elliptic Problem

The singular semilinear elliptic equation Δu + p(x)f(u) = 0 is shown to have a unique positive classical solution inRnthat decays to zero at ∞ ifp(x) is simply a nontrivial nonnegative continuous function satisfying ∫∞0 t max|x| = t p(x) dt < ∞, providedfis a non-increasing continuously differentiable function on (0, ∞). It is also shown that the equation has a unique weakH10-solution on a bounded domain provided ∫e0 f(s) ds < ∞ andp(x) ∈ L2.

Alan V. Lair | Aihua W. Shaker | A. W. Shaker | A. Lair | A. V. Lair

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