A discontinuous nonlinear eigenvalue/Free boundary problem

摘要

AbstractWe study the problemdocumentclass{article}pagestyle{empty}begin{document}$$ begin{array}{*{20}c} { - Delta u = lambda H({rm u - 1)}} & {{rm in }Omega } {u = g} & {{rm in }partial Omega } end{array} $$end{document}(His the Heaviside unit step function) in spherical domains Ω of arbitrary dimension. Wheng= 0, there are two branches of radial solutions; for small nonzerogthere are solutions near the corresponding radial solution. Moreover, the set where μ = 1 is in all cases an analytic hypersurfac