Patterns of Non-Radial Solutions to Coupled Semilinear Elliptic Systems on a Disc

2020/02/09 by Zalman Balanov, Balanov, Z., Edward Hooton +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2002.03462

openalex publication_date 2020/02/09 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the existence of non-radial solutions to the problem -\triangle u=f(z,u), u|_{∂ D}=0 on the unit disc D:=\z∈ \mathbb C : |z|<1\ with u(z)∈ \mathbb R^k, where f is a sub-linear continuous function, differentiable with respect to u at zero and satisfying f(e^iθz,u) = f(z,u) for all θ∈ \mathbb R, f(z,-u)=- f(z,u). Under the assumption that f respects additional (spacial) symmetries on \mathbb R^k, we investigate symmetric properties of the corresponding non-radial solutions. The abstract result is supported by a numerical example with extra S₄-symmetries.

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• Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Unit Ball in \mathbb R³ and Their Patterns

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