Title

Classical and Weak Solutions of a Singular Semilinear Elliptic Problem

Document Type

Article

Publication Date

7-15-1997

Abstract

The singular semilinear elliptic equation Δu + p(x)f(u) = 0 is shown to have a unique positive classical solution in Rn that decays to zero at ∞ if p(x) is simply a nontrivial nonnegative continuous function satisfying ∫0 t max|x| = t p(x) dt < ∞, provided f is 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 ∫ε0 f(s) ds < ∞ and p(x) ∈ L2.

Comments

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Reviewed at MR1458503

DOI

10.1006/jmaa.1997.5470

Source Publication

Journal of Mathematical Analysis and Applications

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