Multiple positive solutions of the stationary Keller-Segel system

DOI10.1007/s00526-017-1163-3zbMath1375.35097arXiv1603.07374OpenAlexW2311576534MaRDI QIDQ2403770

Benedetta Noris, Jean-Baptiste Castéras, Denis Bonheure

Publication date: 12 September 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.07374

zbMATH Keywords

radial solutionsradial bifurcationsstationary Keller-Segel equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Bifurcations in context of PDEs (35B32) Semilinear elliptic equations (35J61)

Related Items (15)

Stationary solutions to the Keller–Segel equation on curved planes ⋮ Supercritical problems via a fixed point argument on the cone of monotonic functions ⋮ Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions ⋮ Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions ⋮ A new variational principle, convexity, and supercritical Neumann problems ⋮ A \(p\)-Laplacian supercritical Neumann problem ⋮ Layered solutions with unbounded mass for the Keller-Segel equation ⋮ A general existence result for stationary solutions to the Keller-Segel system ⋮ Singular radial solutions for the Keller-Segel equation in high dimension ⋮ A priori bounds and multiplicity of positive solutions for p-Laplacian Neumann problems with sub-critical growth ⋮ Unbounded mass radial solutions for the Keller-Segel equation in the disk ⋮ Free boundary problems arising in the theory of maximal solutions of equations with exponential nonlinearities ⋮ Perturbative techniques for the construction of spike-layers ⋮ Maximal solution of the Liouville equation in doubly connected domains ⋮ Supercritical elliptic problems on nonradial domains via a nonsmooth variational approach

Uses Software

• AUTO
• AUTO-07P
• DLMF

Cites Work

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