A multiplicity theorem for double phase degenerate Kirchhoff problems

In this paper, we consider a nonlinear elliptic equation involving a nonlocal term which vanishes at finitely many points, a nonhomogeneous partial differential operator (called double phase differential operator) which satisfies unbalanced growth, and a nonlinear function. Such nonlinear elliptic equation is called double phase degenerate Kirchhoff problem (DPDKP, for short). The major contribution of this paper is to establish a multiplicity theorem for (DPDKP) in which our main method is based on truncation technique and variational method.