Multiple normalized solutions for a planar gauged nonlinear Schrodinger equation

作者：Luo, Xiao^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2018, 69(3): 58.

DOI：10.1007/s00033-018-0952-7

• Gauged Schrodinger equation
• Normalized solutions
• Multiplicity
• Asymptotic behavior

We study the existence, multiplicity, quantitative property and asymptotic behavior of normalized solutions for a gauged nonlinear Schrodinger equation arising from the Chern-Simons theory @@@ -Delta u + omega u + vertical bar x vertical bar(2)u + lambda (h(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) +integral(+infinity)(vertical bar x vertical bar) h(s)/s u(2)(s)ds) u = vertical bar u vertical bar(p-2)u, x is an element of R-2, @@@ where omega is an element of R, lambda > 0, p > 4 and @@@ h(s) = 1/2 integral(s )(0)ru(2)(r) dr. @@@ Combining constraint minimization method and minimax principle, we prove that the problem possesses at least two normalized solutions: One is a ground state and the other is an excited state. Furthermore, the asymptotic behavior and quantitative property of the ground state are analyzed.

• 出版日期2018-6
• 单位华中师范大学