Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774179 | Journal of Differential Equations | 2017 | 17 Pages |
Abstract
We prove the existence of monotone heteroclinic solutions to a scalar equation of the kind uâ³=a(t)Vâ²(u) under the following assumptions: VâC2(R) is a non-negative double well potential which admits just one critical point between the two wells, a(t) is measurable, asymptotically periodic and such that infâ¡a>0, supâ¡a<+â. In particular, we improve earlier results in the so called asymptotically autonomous case, when the periodic part of a, say aË, is constant, i.e. a(t) converges to a positive value l as |t|â+â. Furthermore, whenever aË fulfils a suitable non-degeneracy condition, the solutions are shown to be infinitely many.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Andrea Gavioli,