Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (2): 433-446.

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Existence and Multiplicity of Radial Solutions for Double Phase Problem on the Entire Space RN

Ge Bin(),Yuan Wenshuo()   

  1. College of Mathematical Sciences, Harbin Engineering University, Harbin 150001
  • Received:2021-08-05 Revised:2022-04-25 Online:2023-04-26 Published:2023-04-17
  • Supported by:
    National Natural Science Foundation of China(11201095);Fundamental Research Funds for the Central Universities(3072022TS2402);Postdoctoral Research Startup Foundation of Heilongjiang(LBH-Q14044);Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province(LC201502)

Abstract: This study is concerned with the following double phase problem div(|u|p2u+μ(x)|u|q2u)+|u|p2u+μ(x)|u|q2u=λf(x,u),xRN, where 1 < p < q < N, qp1+αN, λ is a real parameter, 0μC0,α(RN) with α(0,1] and f:RN×RR satisfies a Carathéodory condition. The aim is to determine the precise positive interval of λ for which the problem admits at least one or two nontrivial radially symmetric solutions by applying abstract critical point results.

Key words: Double phase operator, Radially symmetric solutions, Critical point theorems, Variational methods

CLC Number: 

  • O175
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