Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain

Abstract

We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.

Multiple critical points of saddle geometry functionals

“…However, from the biological point of view (e.g., fishery management problems) there are natural reasons why the spatial sources or sinks should be involved, for example predation or harvesting of the species could happen. The problems with logistic growth and constant yield harvesting modeled by f (x) < 0, x ∈ Ω, in (5.2) or its stationary version (5.1) have been recently studied in many papers, see, e.g., S. Oruganti, J. Shi, R. Shivaji [26] or P. Liu, J. Shi, Y. Wang [21].…”

“…They point out that these problems could be mathematically challenging. For example, the existence of positive solutions which is natural specifically in biological models is intensively studied (see, e.g., S. Oruganti, J. Shi, R. Shivaji [26], P. Liu, J. Shi, Y. Wang [21] again).…”

“…Lately, P. Liu, J. Shi, Y. Wang [21] studied the exact multiplicity of solutions and obtained precise bifurcation diagrams for this problem on symmetric domains. Hence, Thm.…”