Constraint Minimizers of Kirchhoff-Schrodinger Energy Functionals with L2-Subcritical Perturbation

In this paper, we study the constrained minimization problem (1.1) of the Kirchhoff-Schrodinger energy functional under an L-2-subcritical perturbation. The existence and nonexistence of constraint minimizers are completely classified in terms of the L-2-subcritical exponent q. Especially for q is an element of (4/3, 8/3), we prove that there exists a critical value beta* such that (1.1) has no minimizer if the coefficient beta of L-2 - critical term satisfies beta = beta*. For q is an element of (4/3, 8/3), the blow-up behavior of minimizers as beta NE arrow beta* are also analyzed rigorously if the coefficient lambda of L-2-subcritical term satisfies lambda > lambda(0), where lambda(0) is a positive constant.