On coupled Schrödinger systems with double critical exponents and indefinite weights

الأصل · EN

By using variational methods, we study the existence of mountain pass solution to the following doubly critical Schrödinger system: cases -Δu-μ₁u/|x|²-|u|²*⁻²u &=h(x)α|u|α⁻²|v|βu in ⁿ, -Δv-μ₂v/|x|²-|v|²*⁻²v &= h(x)β|u|α|v|β⁻²v in ⁿ, cases where α≥ 2, β≥ 2, α+β≤ 2*; μ₁, μ₂∈ [0, (N-2)²/4). The weight function h(x) is allowed to be sign-changing so that the nonlinearities include a large class of indefinite weights. We show that the PS condition is satisfied at higher energy level when α+β=2* and obtain the existence of mountain pass solution. Besides, a nonexistence result of the ground state is given.