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Nonradial large solutions of sublinear elliptic problems
Authors:Khalifa El Mabrouk  Wolfhard Hansen
Institution:aDepartment of Mathematics, Faculty of Sciences of Monastir, 5019 Monastir, Tunisia;bFakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
Abstract:Let p be a nonnegative locally bounded function on View the MathML source, Ngreater-or-equal, slanted3, and 0<γ<1. Assuming that the oscillation sup|x|=rp(x)−inf|x|=rp(x) tends to zero as r→∞ at a specified rate, it is shown that the equation Δu=p(x)uγ admits a positive solution in View the MathML source satisfying lim|x|→∞u(x)=∞ if and only if
View the MathML source
Keywords:Large solution  Semilinear Dirichlet problem  Greenian domain  Green function
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