Generating loops and isolas in semilinear elliptic BVP's

Abstract

In this paper, we ascertain the global ?-structure of the set of positive and negative solutions bifurcating from u=0 for the semilinear elliptic BVP-dAu=Ya,Au+u+u2uqin,u=0on,according to the values of d>0 and the integer number q4. Figs. 1.1-1.3 summarize the main findings of this paper according to the values of d and q. Note that the role played by the parameter Y in this model is very special, because, besides measuring the strength of the convection, it quantifies the amplitude of the nonlinear term Yu2. We regard to this problem as a mathematical toy to generate solution loops and isolas in Reaction Diffusion equations.