Mirroring in lattice equations and a related functional equation
We use a functional form of the mirroring technique to fully characterize equivalence classes of unbounded stationary solutions of lattice reaction-diffusion equations with eventually negative and decreasing nonlinearities. We show that solutions which connect a stable fixed point of the nonlinearit...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2024
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Nagumo-egyenlet, Rácsdifferenciálegyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2024.1.65 |
| Online Access: | http://acta.bibl.u-szeged.hu/88867 |
| Tartalmi kivonat: | We use a functional form of the mirroring technique to fully characterize equivalence classes of unbounded stationary solutions of lattice reaction-diffusion equations with eventually negative and decreasing nonlinearities. We show that solutions which connect a stable fixed point of the nonlinearity with infinity can be characterized by a single parameter from a bounded interval. Within a two-dimensional parametric space, these solutions form a boundary to an existence region of solutions which diverge in both directions. Additionally, we reveal a natural relationship of lattice equations with an interesting functional equation which involves an unknown function and its inverse. |
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| Terjedelem/Fizikai jellemzők: | 21 |
| ISSN: | 1417-3875 |