A remark on the existence of large solutions via sub and supersolutions
Date
2003-11-04
Authors
Garcia-Melian, Jorge
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We study the boundary blow-up elliptic problem ∆u = α(x)ƒ(u) in a smooth bounded domain Ω ⊂ ℝN, with u|∂Ω = +∞. Under suitable growth assumptions on α near ∂Ω 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 ƒ(u) at infinity and on the other hand positive weights α(x) which are unbounded and/or oscillatory near the boundary.
Description
Keywords
Boundary blow-up, Sub and supersolutions
Citation
Garcia-Melian, J. (2003). A remark on the existence of large solutions via sub and supersolutions. <i>Electronic Journal of Differential Equations, 2003</i>(110), pp. 1-4.
Rights
Attribution 4.0 International