✦ LIBER ✦
Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states
✍ Scribed by Philippe Souplet; Qi S. Zhang
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 163 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0294-1449
No coin nor oath required. For personal study only.
✦ Synopsis
with 1 < p < n+2 n-2 , n 2, and 0 V (x) ∈ L ∞ , which may decay to 0 at infinity. We prove that if V is radial and satisfies
then (1) admits a (ground state) positive solution. We do not use traditional variational methods and the result relies on the study of global solutions of the parabolic problem
(2) Indeed, we will show that, under suitable conditions on V (not necessarily radial), (2) admits global positive solutions and that when V and u 0 are radial some global solutions have ωlimit sets containing a positive equilibrium. The method also covers nonlinearities more general