Least Energy Solutions of the Schrödinger–Kirchhoff Equation with Linearly Bounded Nonlinearities.

In this paper, we consider the following Schrödinger–Kirchhoff equation - a + b ∫ R N | ∇ u | 2 d x Δ u + V (x) u = f (x , u) , in R N , <graphic href="12346_2023_859_Article_Equ54.gif"></graphic> where N ≥ 3 , a and b are positive parameters, V(x) is a positive and continuous potential. Under some suitable assumptions on the nonlinearity f(x, u) which allow it is linearly bounded at infinity, the existence of least energy solutions and their asymptotic behavior as b → 0 are established via variational methods. The nonexistence of nontrivial solutions is also established for large b. [ABSTRACT FROM AUTHOR]