We study systems of elliptic equations −∆u(x)+Fu(x, u) = 0 with potentials F ∈ C2(Rn,Rm) which are periodic and even in all their variables. We show that if F(x,u) has flip symmetry with respect to two of the compo- nents of x and if the minimal periodic solutions are not degenerate then the system has saddle type solutions on Rn
SADDLE SOLUTIONS FOR A CLASS OF SYSTEMS OF PERIODIC AND REVERSIBLE SEMILINEAR ELLIPTIC EQUATIONS / Alessio, Francesca Gemma; Montecchiari, Piero; Sfecci, Andrea. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 14:3(2019), pp. 569-589. [10.3934/nhm.2019022]
SADDLE SOLUTIONS FOR A CLASS OF SYSTEMS OF PERIODIC AND REVERSIBLE SEMILINEAR ELLIPTIC EQUATIONS
Francesca Gemma Alessio;Piero Montecchiari
;Andrea Sfecci
2019-01-01
Abstract
We study systems of elliptic equations −∆u(x)+Fu(x, u) = 0 with potentials F ∈ C2(Rn,Rm) which are periodic and even in all their variables. We show that if F(x,u) has flip symmetry with respect to two of the compo- nents of x and if the minimal periodic solutions are not degenerate then the system has saddle type solutions on RnFile in questo prodotto:
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