Normalized Solutions Of Kirchhoff Type Equations

In this paper, we study the existence of solutions with prescribed L2-norm for a class of Kirchhoff type problems in R3where a,b>0are constants, p∈(14/3,6). To obtain such solutions we look for critical points of the energy functional on the constraints given by For the value p∈(14/3,6) considered, the functional F is unbounded from below on S(c) and the existence of critical points is obtained by a mountain pass argument on S(c). We show that critical points exist for any fixed c>0. Finally, inspired by some recent works of Bartch and De Valeriola [8] and Luo [23], we prove a multiplicity result of normalized solutions for our problems.