Existence of additional unstable equilibria for some monostable systems

✍ Scribed by E.C.M. Crooks

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 342 KB
• Volume: 67
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.08.034

✦ Synopsis

We prove the existence of additional unstable equilibria E ± for a class of "monostable" reaction-diffusion systems

having known equilibria S < T with S "stable" and T "unstable" such that the derivative d f [T ] has an even number of unstable eigenvalues. The proofs use positive-operator theory and degree theory. Systems in the class considered are known to admit monotone increasing travelling-wave solutions w(xct) connecting ordered stable and unstable equilibria for all c greater than or equal to a positive critical value and the existence of E ± > S yields two one-parameter families of travelling waves connecting S to E ± in addition to the family connecting S to T .