Semi-linear cooperative elliptic systems involving Schrödinger operators: Groundstate positivity or negativity..

Bénédicte Alziary , Jacqueline Fleckinger (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study here the behavior of the solutions to a 2×2 semi-linear cooperative system involving Schrödinger operators (considered in its variational form): LU := (−∆ + q(x))U = AU + µU + F (x, U) in R N U (x) |x|→∞ → 0 where q is a continuous positive potential tending to +∞ at infinity; µ is a real parameter varying near the principal eigenvalue of the system; U is a column vector with components u 1 and u 2 and A is a square cooperative matrix with constant coefficient. F is a column vector with components f 1 and f 2 depending eventually on U .

Domaines: Equations aux dérivées partielles [math.AP]

Bénédicte Alziary, Jacqueline Fleckinger. Semi-linear cooperative elliptic systems involving Schrödinger operators: Groundstate positivity or negativity... Rostocker Mathematisches Kolloquium, 2017. ⟨hal-01976893⟩