Infinitely many stationary solutions for a simple climate model via a shooting method

Abstract

In this paper, we study the number of steady solutions of a non-linear model arising in Climatology. By applying a shooting method we show the existence of infinitely many steady solutions for some values of a parameter (the solar constant). This method allows us to determine how many times a solution attains the critical temperature (-10degreesC) at which the coalbedo is assumed to be discontinuous.