We study systems of elliptic equations -Δ 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 components 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
Sfecci A.
2019-01-01
Abstract
We study systems of elliptic equations -Δ 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 components of x and if the minimal periodic solutions are not degenerate then the system has saddle type solutions on ℝn.File in questo prodotto:
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