Bifurcation to positive solutions in BVPs of logistic type with nonlinear indefinite mixed boundary conditions

Abstract

In this paper a nonlinear boundary value problem of logistic type is considered, with nonlinear mixed boundary conditions, and with spatial heterogeneities of arbitrary sign in the differential equation and on the boundary conditions. The main goal of this paper is analyzing the structure of the continuum of positive solutions emanating from the trivial state at a unique bifurcation value, depending on the size and sign of the different potentials and parameters of the problem. The results in this paper extend the previous ones obtained by R. Gomez-Renasco and J. Lopez-Gomez [5, Proposition 2.1], for a superlinear indefinite problem of logistic type under Dirichlet boundary conditions, to a wide class of superlinear indefinite problems with nonlinear indefinite mixed boundary conditions.