We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimension N and the two exponents, 0 < α < β < 1, of the involved nonlinearites. Suitable assumptions are made on the spatial domain Ω where the problem is formulated in order to avoid a possible continuum of those solutions and, on the contrary, to ensure the exact number of solutions according to the nature of the domain

more »

... Our results also clarify some previous works in the literature. The main techniques of proof are a Pohozhaev's type identity and some fibering type arguments in the variational approach.