Normalized Solutions of Nonautonomous Kirchhoff Equations: Sub- and Super-critical Cases

Abstract

In this paper, we establish the existence of normalized solutions to the following Kirchhoff-type equation {-(a+b∫R3|∇u|2dx)Δu-λu=K(x)f(u),x∈R3;u∈H1(R3),where a, b> 0 , λ is unknown and appears as a Lagrange multiplier, K∈ C(R3, R+) with 0