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 ...

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance ...

In this article, we study a fractional control problem that models the maximization of the profit obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the ...

This study proposes a delay-coupled system based on the logistic equation that models the interaction of a population with its varying environment. The integro-diferential equations of the model are presented in terms of ...

Let Ω be a smooth bounded domain in RN, N≥1, let m,n be two nonnegative functions defined in Ω and let ϕ:RN→RN be a continuous and strictly monotone mapping. We consider the existence and nonexistence of positive solutions ...

This paper discusses the modeling via mathematical methods based on fractional calculus, using Caputo fractional derivative. From the fractional models associated with harmonic oscillator, logistic equation and Malthusian ...