Bifurcation and stability for diffusive logistic equations with nonlinear boundary conditions

Abstract

In this note we study a semilinear elliptic boundary value problem of one parameter dependence which arises in population genetics, having nonlinear boundary conditions. For some cases of sign indefinite weights, we investigate the existence and asymptotic behavior of the minimal positive solution. The analysis uses the local bifurcation theory from simple eigenvalues, super-sub-solution method and variational technique.