首页|The Complementarity of Normalized Solutions for Kirchhoff Equations with Mixed Nonlinearity
The Complementarity of Normalized Solutions for Kirchhoff Equations with Mixed Nonlinearity
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In this paper,we study the existence of solutions for Kirchhoff equation-(a+b∫(R)3|▽u|2dx)△u=λu+μ|u|q-2u+|u|p-2u,x ∈(R)3 with mass constraint condition Sc:={u ∈ H1((R)3):∫(R)3|u|2dx=c},where a,b,c＞0,μ ∈(R),2＜q＜p＜6,and λ ∈(R)appears as a Lagrange multiplier.For the range of p and q,the Sobolev critical exponent 6 and mass critical exponent 14/3 are involved where corresponding energy functional is unbounded from below on Sc.We consider the focusing case,i.e.,μ＞0 when(p,q)belongs to a certain domain in (R)2.We prove the existence of normalized solutions by using constraint minimization,concentration compactness principle and Minimax methods.We partially extend the results which have been studied.
normalized solutionsKirchhoff type equationmixed nonlinearty
Lin XU、Qilin XIE
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School of Mathematics and Statistics,Guangdong University of Technology,Guangdong 510520,P.R.China
Basic and Applied Basic Research Foundation of Guangdong Province
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