We establish the complete bifurcation diagram for a class of nonlinear problems on the whole space. Our model corresponds to a class of semilinear elliptic equations with logistic type nonlinearity and absorption. Since this problem arises in population dynamics or in fishery or hunting management, we are interested only in situations allowing the existence of positive solutions. The proofs combine elliptic estimates with the method of sub- and super-solutions. The journal is very high on the Science Citation Index list, in the year 2008 it placed the 15th among 214 journals.

COBISS.SI-ID: 15094617

Let X be a finite spectrum. We prove that R(X_{(p)}), the endomorphism ring of the p-localization of X, is a semi-perfect ring. This implies, among other things, a strong form of unique factorization for finite p-local spectra. The main step in the proof is that the Jacobson radical of R(X_{(p)}) is idempotent-lifting, which is proved by a combination of geometric properties of finite spectra and algebraic properties of the p-localization.

COBISS.SI-ID: 15179097