Generating loops and isolas in semilinear elliptic BVP’s

Abstract

In this paper, we ascertain the global λ-structure of the set of positive and negative solutions bifurcating from u=0 for the semilinear elliptic BVP −dΔu=λ〈a,∇u〉+u+λu2−uqinΩ,u=0on∂Ω,according to the values of d>0 and the integer number q≥4. 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 λ in this model is very special, because, besides measuring the strength of the convection, it quantifies the amplitude of the nonlinear term λu2. We regard to this problem as a mathematical toy to generate solution loops and isolas in Reaction Diffusion equations.