Multiple solutions to Gierer-Meinhardt systems of elliptic equations
Abdelkrim Moussaoui
TL;DR
This paper proves the existence of multiple solutions for Gierer-Meinhardt elliptic systems with Neumann boundary conditions using sub-supersolution and topological degree methods.
Contribution
It introduces a novel combination of sub-supersolution and Leray-Schauder degree techniques to establish multiple solutions for these systems.
Findings
Multiple solutions are proven to exist for the Gierer-Meinhardt system.
The methods used can be applied to similar elliptic systems.
Neumann boundary conditions are effectively handled.
Abstract
We establish the existence of multiple solutions for Gierer-Meinhardt system involving Neumann boundary conditions. The approach combines the methods of sub-supersolution and Leray-Schauder topological degree.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Differential Equations and Numerical Methods