Nodal solutions with synchronous sign changing components and Constant sign solutions for singular Gierer-Meinhardt type system

2023/06/29 by Abdelkrim Moussaoui, Moussaoui, Abdelkrim
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.16742

openalex publication_date 2023/06/29 · openalex created_date 2023/07/01 · openalex updated_date 2026/07/28

Abstract

We establish the existence of three solutions for singular semilinear elliptic system, two of which are of opposite constant-sign. Under a strong singularity effect, the third solution is nodal with synchronous sign components. The approach combines sub-supersolutions method and Leray-Schauder topological degree involving perturbation argument.

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