Large solutions to non-monotone semilinear elliptic systems

• DOI: 10.1016/j.jmaa.2011.05.061
• Publication Date: 2011-06-05T14:39:19Z
• Authors: Jesse D. Peterson; Aihua W. Wood
• Keywords: Semilinear elliptic systems; Applied Mathematics; Large solutions; 0101 mathematics; 01 natural sciences; Analysis

AbstractWe present the existence of entire large positive radial solutions for the non-monotonic system Δu=p(|x|)g(v), Δv=q(|x|)f(u) on Rn where n⩾3. The functions f and g satisfy a Keller–Osserman type condition while nonnegative functions p and q are required to satisfy the decay conditions ∫0∞tp(t)dt<∞ and ∫0∞tq(t)dt<∞. Further, p and q are such that min(p,q) does not have compact support.