Normalized Ground State Solutions for Nonautonomous Choquard Equations.

In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation where c > 0, 0 < μ < N, λ ∈ ℝ, A ∈ C1 (ℝN, ℝ). For p ∈ (2*,μ, p ¯ , we prove that the Choquard equation possesses normalized ground state solutions, and the set of ground states is orbitally stable. For p ∈ (p ¯ , 2 μ ∗) , we find a normalized solution, which is not a global minimizer. 2*μ and 2*,μ are the upper and lower critical exponents due to the Hardy–Littlewood–Sobolev inequality, respectively. p ¯ is the L2-critical exponent. Our results generalize and extend some related results. [ABSTRACT FROM AUTHOR]