Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equations
The authors obtain a result concerning the limit of certain sequences of principal eigenvalues associated with some elliptic eigenvalue problems. The result allows to give a complete description of the global structure of the curves of positive steady states of a parameter dependent diffusive version of the classical logistic equation. The stability of the positive steady states and the asymptotic behaviour of positive solutions are also discussed.
scientific article; zbMATH DE number 881711