Generating loops and isolas in semilinear elliptic BVP's. (July 2023) - López-Gómez, Julián; Sampedro, Juan Carlos
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 − d Δ u = λ 〈 a, ∇ u 〉 + u + λ u 2 − u q in Ω, u = 0 on ∂ 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 λ u 2 . We regard to this problem as a mathematical toy to generate solution loops and isolas in Reaction Diffusion equations.