Logistic equation with Robin type boundary conditions and undefined coefficients.
super – and subsolution, principal eigenvalues, Lagrange multipliers, logistic equation.
In this work, we consider a logistic equation with boundary flux arising from a population dynamics
model. We prove the existence and uniqueness of a positive solution, as well as establish some qualitative properties.
To this end, we conduct a study of an eigenvalue problem with indefinite coefficients using variational methods. Then,
we apply the method of sub- and supersolution.