The existence and nonexistence of global L2-constrained minimizers for Kirchhoff equations with L2-subcritical general nonlinearity

作者：Ye, Hongyu^*; Zhang, Lina

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46(5): 5234-5244.

DOI：10.1002/mma.8827

• constrained minimization
• global L-2-constraint minimizers
• L-2-subcritical general nonlinearity
• subadditivity inequality

In this paper, we study the existence of global L2-constrained minimizers related to the following Kirchhoff type equation: @@@ - ( a + b integral (N)(R) vertical bar del u vertical bar(2) ) Delta u - f(U) = lambda u, x epsilon R-N , lambda epsilon R, @@@ where N <= 3, a, b > 0 are constants, f(u) is a general L-2-subcritical nonlinearity. By using the concentration compactness principle, we prove the sharp existence and nonexistence of global L-2- constraint minimizers.