Multiplicity of solutions for a critical nonlinear Schrödinger–Kirchhoff-type equation

AbstractIn this paper, we study the following critical nonlinear Schrödinger–Kirchhoff equation: ($P$) {−(a+b∫RN|∇u|2dx)Δu+V(x)u=P(x)|u|2∗−2u+μ|u|q−2u, in RN,u∈H1(RN)($P$) where a,b,μ>0, N≥3, max{2∗−1,2}0 and P(x)≥0 are two continuous functions. By using the variational method and truncation technique, we prove the multiplicity of solutions for Equation (P).Keywords: Schrödinger–Kirchhoff equationcritical exponentlocal Pohozaev identitiesmultiplicity of solutions2020 Mathematics Subject Classifications: 35J1047J30 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by the National Natural Science Foundation of China [grant numbers 12261031, 12261076, 11801545] and the Fundamental Research Funds for the Central Universities [grant number 2023MS078].