Entire solutions in for a class of Allen-Cahn equations
Dipartimento di Scienze
Matematiche, Università Politecnica delle Marche, via
Brecce Bianche, 60131 Ancona, Italy; email@example.com;firstname.lastname@example.org
We consider a class of semilinear elliptic equations of the form 15.7cm - where , is a periodic, positive function and is modeled on the classical two well Ginzburg-Landau potential . We look for solutions to ([see full textsee full text]) which verify the asymptotic conditions as uniformly with respect to . We show via variational methods that if ε is sufficiently small and a is not constant, then ([see full textsee full text]) admits infinitely many of such solutions, distinct up to translations, which do not exhibit one dimensional symmetries.
Mathematics Subject Classification: 34C37 / 35B05 / 35B40 / 35J20 / 35J60
Key words: Heteroclinic solutions / elliptic equations / variational methods.
© EDP Sciences, SMAI, 2005