Classical and Weak Solutions of a Singular Semilinear Elliptic Problem

Authors

Alan V. Lair, Air Force Institute of TechnologyFollow
Aihua W. Shaker, Air Force Institute of Technology

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

Copyright © 1997 Academic Press. All rights reserved.

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Reviewed at MR1458503

DOI

10.1006/jmaa.1997.5470

Source Publication

Journal of Mathematical Analysis and Applications

Recommended Citation

Lair, A. V, & Shaker, A. W. (1997). Classical and Weak Solutions of a Singular Semilinear Elliptic Problem. Journal of Mathematical Analysis and Applications, 211(2), 371–385. https://doi.org/10.1006/jmaa.1997.5470