Study of a logistic equation with local and non-local reaction terms - Delgado, Manuel; Figueiredo, Giovany M.; Pimenta, Marcos T. O. [UNESP]; Suárez, Antonio (Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University, 2016)
We examine a logistic equation with local and non-local reaction terms both for time dependent and steady-state problems. Mainly, we use bifurcation and monotonicity methods to prove the existence of positive solutions for the steady-state equation and sub-supersolution method for the long time behavior for the time dependent problem. The results depend strongly on the size and sign of the parameters on the local and non-local terms.
Keywords: Bifurcation methods; Local and non-local terms; Logistic equation