The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations
Hongyu Ye
Source abstract
In this paper, we study the existence of solutions with prescribed L 2 ‐norm for the following Kirchhoff type equation: urn:x-wiley:mma:media:mma3247:mma3247-math-0001 where N ≤3, a , b > 0 are constants, p ∈(2,2*),2*=6 if N = 3, and 2*=+ ∞ if N = 1,2. We obtain the sharp existence of global constraint minimizers for . In the case , the existence of solutions with prescribed L 2 ‐norm is obtained for all L 2 ‐norm. The key point is the analysis of excluding the dichotomy of the minimizing sequences for the related constrained minimization problem. Copyright © 2014 John Wiley & Sons, Ltd.
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