A remark on the existence of large solutions via sub and supersolutions

• Main Author: Jorge Garcia-Melian
• Format: Article
• Language: English
• Published: Texas State University 2003-11-01
• Series: Electronic Journal of Differential Equations
• Subjects: Boundary blow-up; sub and supersolutions
• Online Access: http://ejde.math.txstate.edu/Volumes/2003/110/abstr.html

We study the boundary blow-up elliptic problem $Delta u=a(x) f(u)$ in a smooth bounded domain $Omegasubset mathbb{R}^N$, with $u|_{partialOmega}=+infty$. Under suitable growth assumptions on $a$ near $partialOmega$ and on $f$ both at zero and at infinity, we prove the existence of at least a positive solution. Our proof is based on the method of sub and supersolutions, which permits on the one hand oscillatory behaviour of $f(u)$ at infinity and on the other hand positive weights $a(x)$ which are unbounded and/or oscillatory near the boundary.