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Paper's Title:

Existence of Large Solutions to Non-Monotone Semilinear Elliptic Equations

Author(s):

Alan V. Lair, Zachary J. Proano, and Aihua W. Wood

Air Force Institute of Technology
2950 Hobson Way, AFIT/ENC
Wright-Patterson Air Force Base, OH, 45433-7765,
USA.
Aihua.Wood@afit.edu
URL: www.afit.edu


Abstract:

We study the existence of large solutions of the semilinear elliptic equation Δu=p(x)f(u) where f is not monotonic. We prove existence, on bounded and unbounded domains, under the assumption that f is Lipschitz continuous, f(0) = 0, f(s) > 0 for s > 0 and there exists a nonnegative, nondecreasing Hölder continuous function g and a constant M such that g(s) ≤ f(s) ≤ Mg(s) for large s. The nonnegative function p is allowed to be zero on much of the domain.


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