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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 14
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Research Article

A perturbed problem of elliptic system with critical exponent

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Pages 4982-4990 | Received 09 Jun 2020, Accepted 12 Jan 2021, Published online: 27 Jan 2021

References

  • Abdellaoui B, Felli V, Peral I. Some remarks on systems of elliptic equations doubly critical in the whole RN. Calc Var Partial Differ Equ. 2009;34(1):97–137.
  • Chen Z, Zou W. Positive least energy solutions and phase seperation for coupled Schrödinger equations with critical exponent. Arch Ration Mech Anal. 2012;205(2):515–551.
  • Chen Z, Zou W. Positive least energy solutions and phase seperation for coupled Schrödinger equations with critical exponent: higher dimensional case. Calc Var Partial Differ Equ. 2015;52(1-2):423–467.
  • Chen Z, Zou W. Existence and symmetry of positive ground states for a doubly critical schrödinger system. Trans Amer Math Soc. 2015;367(5):3599–3646.
  • Li Q. The perturbation problem of an elliptic system with Sobolev critical growth. Acta Math. Sci. Ser. B (Engl. Ed.) 2020;40(5): 1391–1404.
  • Peng S, Wang Q, Wang Z-Q. On coupled nonlinear Schrödinger systems with mixed couplings. Trans Amer Math Soc. 2019;371(11):7559–7583.
  • Peng S, Shuai W, Wang Q. Multiple positive solutions for linearly coupled nonlinear elliptic systems with critical exponent. J Differ Equ. 2017;263(1):709–731.
  • Peng S, Peng Y, Wang Z-Q. On elliptic systems with sobolev critical growth. Calc Var Partial Differ Equ. 2016;55(6):63. Art 142, 30 pp.
  • Peng S, Wang Z-Q. Segregated and synchronized vector solutions for nonlinear schrödinger system. Arch Rational Mech Anal. 2013;208(1):305–339.
  • Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical sobolev exponents. Commun Pure Appl Math. 1983;36(4):437–477.
  • Aubin T. Problemes isoperimetriques et espaces de sobolev. J Differ Geom. 1976;11(4):573–598.
  • Swanson C. The best Sobolev constant. Appl Anal. 1992;47(4):227–239.
  • Talenti G. Best constant in Sobolev inequality. Ann Mat Pure Appl. 1976;110(1):353–372.
  • Chen Z, Zou W. A remark on doubly critical elliptic systems. Calc Var Partial Differ Equ. 2014;50(3-4):939–965.
  • Pistoia A, Soave N. On Coron's problem for weakly coupled elliptic systems. Proc Lond Math Soc. 2018;116(1):33–67.
  • Pistoia A, Soave N, Tavares H. A fountain of positive bubbles on a coron's problem for a competitive weakly coupled gradient system. J Math Pures Appl. 2020;135:159–198.
  • Ambrosetti A, Garcia Azorero J, Peral I. Perturbation of Δu+u(N+2)/(N−2)=0, the scalar curvature problem in RN and related topics. J Funct Anal. 1999;165(1):117–149.
  • Cao D, Noussair E S, Yan S. On the scalar curvature equation −Δu=(1+ϵK)u(N+2)/(N−2) in RN. Calc Var Partial Differ Equ. 2002;15(3):403–419.

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