Qualitative Properties of Positive Solutions of Elliptic Equations

This talk is intended as a survey of recent results about qualitative properties for positive solutions of semilinear elliptic equations of the type (1.1) Δ u   +   f ( u )   =   0     in     Ω , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203744376/a3a6af35-efd2-43dc-a017-2efeb7a27be6/content/eq289.tif"/> (1.2) u   =   0     on     ∂ Ω https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203744376/a3a6af35-efd2-43dc-a017-2efeb7a27be6/content/eq290.tif"/> in various geometrical settings of unbounded domains Ω. The case of bounded domains will first be recalled in section 2 below.