Unstable Periodic Solutions of a Parabolic Problem in the Presence of Non-well-ordered Lower and Upper Solutions

✍ Scribed by Colette De Coster; Pierpaolo Omari

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 243 KB
• Volume: 175
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3600

✦ Synopsis

We prove the solvability of the Dirichlet-periodic problem for a semilinear parabolic equation, assuming the existence of a lower solution : and an upper solution ;, which do not satisfy the ordering condition : ;. Our results yield the existence of unstable solutions, localized by means of : and ;, requiring weak regularity of the coefficients of the equation.