A mass supercritical problem revisited

In any dimension N ≥ 1 and for given mass m > 0 , we revisit the nonlinear scalar field equation with an L 2 constraint: - Δ u = f ( u ) - μ u in R N , ‖ u ‖ L 2 ( R N ) 2 = m , u ∈ H 1 ( R N ) , ( P m ) where μ ∈ R will arise as a Lagrange multiplier. Assuming only that the nonlinearity f is con...

Celý popis