Nonexistence and Existence of Solutions with Prescribed Norms for Nonlocal Elliptic Equations with Combined Nonlinearities
Nonexistence and Existence of Solutions with Prescribed Norms for Nonlocal Elliptic Equations with Combined Nonlinearities
In this paper, we study the nonlocal equation ∫RN|u(x)|2dxγΔu=λu+μ|u|q−2u+|u|p−2u, xinRN having a prescribed mass ∫RN|u(x)|2dx=c2, where N≥3, μ, γ∈(0,+∞), q∈(2,2∗), c is a positive constant, p, q∈(2,2∗) with p≠q and 2∗=2NN−2. This research is meaningful from a physical point of view. Using variational methods, we present some results on the …