2025/08/20 by João Marcos Ó, Ó, João Marcos do, Evelina Shamarova +3
Medicine · Physics and Astronomy · #35B09 #35J30 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2508.14854
openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/01
We establish existence and multiplicity results for steady-state solutions of spatially heterogeneous FitzHugh-Nagumo-type systems, extending the existing theory from constant to variable coefficients that may change sign. Specifically, we study the system Specifically, we study the system -Δu + a(x)v amp;= f(x,u) amp;amp; in ℝN,
-Δv + b(x)v amp;= c(x)u amp;amp; in ℝN. where N \geqslant 3, the coefficients a,b,c : ℝN → ℝ are L^∞loc-functions bounded from below, and f:ℝN × ℝ → ℝ is a Carathéodory function with subcritical growth. For assumptions permitting sign changes and non-coercivity of the coefficients, we prove the existence of a mountain pass solution. In the case where a,b,c do not change sign, still allowing non-coercive behavior, we additionally establish the existence of componentwise positive and negative solutions.