Blow-Up Behavior of L2-Norm Solutions for Kirchhoff Equation in a Bounded Domain

作者：Zhu, Xincai^*; Zhang, Shu; Wang, Changjian; He, Chunxia

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2023, 46(5): 155.

DOI：10.1007/s40840-023-01548-5

• Kirchhoff equation
• L-2-norm solution
• Minimizer
• Bounded domain
• Blow-up behavior
• Regularity

This paper is devoted to studying the following Kirchhoff equation @@@ - (a + b integral(Omega) vertical bar del u vertical bar(2)dx) Delta u = mu u + beta vertical bar u vertical bar(p)u + lambda vertical bar u vertical bar(q)u, x is an element of Omega @@@ u = 0, x is an element of partial derivative Omega, @@@ where Omega subset of R-3 is a bounded connected domain and integral(Omega) |u|(2)dx = 1. The results of existence and nonexistence on L-2-norm solutions are given. Our argument shows that the blow-up behavior of L-2-norm solution occurs, and the mass concentrates at an inner point of L-2, or the neighborhood of some boundary point.