Ground state normalized solutions to the Kirchhoff equation with general nonlinearities: mass supercritical case.

We study the following nonlinear mass supercritical Kirchhoff equation: − (a + b ∫ R N | ∇ u | 2) △ u + μ u = f (u) in R N , where a , b , m > 0 are prescribed, and the normalized constrain ∫ R N | u | 2 d x = m is satisfied in the case 1 ≤ N ≤ 3 . The nonlinearity f is more general and satisfies weak mass supercritical conditions. Under some mild assumptions, we establish the existence of ground state when 1 ≤ N ≤ 3 and obtain infinitely many radial solutions when 2 ≤ N ≤ 3 by constructing a particular bounded Palais–Smale sequence. [ABSTRACT FROM AUTHOR]