Global branches of positive weak solutions of semilinear elliptic problems over nonsmooth domains
Timothy J. Healey, Hansjörg Kielhöfer, Charles A. Stuart · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1994
We consider the nonlinear eigenvalue problem posed by a parameter-dependent semilinear second-order elliptic equation on a bounded domain with the Dirichlet boundary condition. The coefficients of the elliptic operator are bounded measurable functions and the boundary of the domain is only required to be regular in the sense of Wiener. The main results establish the existence of an unbounded branch of positive weak solutions.