Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 1817-1830.doi: 10.1007/s10473-022-0507-z

• Articles • Previous Articles    

POSITIVE SOLUTIONS FOR A KIRCHHOFF EQUATION WITH PERTURBED SOURCE TERMS

Narimane AISSAOUI1, Wei LONG2   

  1. 1. School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, China;
    2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China
  • Received:2021-03-12 Revised:2022-05-19 Published:2022-11-02
  • Contact: Wei Long,E-mail:lwhope@jxnu.edu.cn E-mail:lwhope@jxnu.edu.cn
  • Supported by:
    The second author was supported by NSF of China (11871253), supported by Jiangxi Provincial Natural Science Foundation (20212ACB201003), Jiangxi Two Thousand Talents Program (jxsq2019101001), Double-high talents in Jiangxi Province and Jiangxi Provincial Department of Education Fund (GJJ191687).

Abstract: This paper deals with the existence of positive solutions to the following nonlinear Kirchhoff equation with perturbed external source terms: {(a+bR3|u|2dx)Δu+V(x)u=Q(x)up+εf(x),xR3,u>0,uH1(R3).

Here a,b are positive constants, V(x),Q(x) are positive radial potentials, 1<p<5, ε >0 is a small parameter, f(x) is an external source term in L2(R3)L(R3).

Key words: nonlinear Kirchhoff problem, Lyapunov-Schmidt reduction, positive solutions, level set

CLC Number: 

  • 35J20
Trendmd