Casey Crane

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math.AP2025

Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Unit Ball in $R^{3}$ and Their Patterns

Casey Crane, Ziad Ghanem

We investigate symmetry-breaking phenomena in semilinear elliptic systems on the unit ball in $R^{3}$ , focusing on the emergence of non-radial solution branches with prescri…

math.AP2025

Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Disc and their Patterns

Ziad Ghanem, Casey Crane

In this paper, we leverage the $O (2) \times Z$ -equivariant Leray-Schauder degree and a novel characterization of the Burnside Ring $A (O (2) \times Z_{2})$ presented by…

math.AP2024

Global Bifurcation of Non-Radial Solutions for Symmetric Sub-linear Elliptic Systems on the Planar Unit Disc

Ziad Ghanem, Casey Crane, Jingzhou Liu

In this paper, we prove a global bifurcation result for the existence of non-radial branches of solutions to the paramterized family of $I^$ -symmetric problems $- I^ u = f (I^\pm, z, u)$ , $u…

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

Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Disc and their Patterns

Global Bifurcation of Non-Radial Solutions for Symmetric Sub-linear Elliptic Systems on the Planar Unit Disc

Unbounded Branches of Non-Radial Solutions to Semilinear Elliptic Systems on a Unit Ball in $R^{3}$ and Their Patterns