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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 17
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Research Article

Kirchhoff equations with indefinite potentials

Lin Lia School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, People's Republic of China;b Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing Technology and Business University, Chongqing, People's Republic of ChinaView further author information
&
Jiafa Xuc School of Mathematical Sciences, Chongqing Normal University, Chongqing, People's Republic of ChinaCorrespondence[email protected]
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Pages 6081-6089 | Received 09 Aug 2019, Accepted 05 Jun 2020, Published online: 29 Apr 2021

References

  • Chen S, Liu S. Standing waves for 4-superlinear Schrödinger-Kirchhoff equations. Math Methods Appl Sci. 2015;38(11):2185–2193.
  • Chen SJ, Li L. Multiple solutions for the nonhomogeneous Kirchhoff equation on RN. Nonlin Anal Real World Appl. 2013;14(3):1477–1486.
  • Cheng B. A new result on multiplicity of nontrivial solutions for the nonhomogenous Schrödinger-Kirchhoff type problem in RN. Mediterr J Math. 2016;13(3):1099–1116.
  • He X, Wu X. Multiple sign-changing solutions for Kirchhoff-type equations in R3. Math Methods Appl Sci. 2018;41(2):512–524.
  • Huang Y, Liu Z. On a class of Kirchhoff type problems. Arch Math (Basel). 2014;102(2):127–139.
  • Li Q, Wu X. A new result on high energy solutions for Schrödinger-Kirchhoff type equations in RN. Appl Math Lett. 2014;30:24–27.
  • Qin D, Liao F, He Y, et al. Infinitely many sign-changing solutions for Kirchhoff-type equations in R3. Bull Malays Math Sci Soc. 2019;42(3):1055–1070.
  • Sun J, Li L, Cencelj M, et al. Infinitely many sign-changing solutions for Kirchhoff type problems in R3. Nonlin Anal. 2019;186:33–54.
  • Wu X. Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in RN. Nonlin Anal Real World Appl. 2011;12(2):1278–1287.
  • Ye Y, Tang CL. Multiple solutions for Kirchhoff-type equations in RN. J Math Phys. 2013;54(8):081508.16.
  • Chen S, Tang X. Infinitely many solutions for super-quadratic Kirchhoff-type equations with sign-changing potential. Appl Math Lett. 2017;67:40–45.
  • Li L, Rădulescu V, Repovš D. Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness. Int J Nonlin Sci Numer Simul. 2016;17(6):325–332.
  • Zhang J, Tang X, Zhang W. Existence of multiple solutions of Kirchhoff type equation with sign-changing potential. Appl Math Comput. 2014;242:491–499.
  • Li SJ, Willem M. Applications of local linking to critical point theory. J Math Anal Appl. 1995;189(1):6–32.
  • Liu S, Wu Y. Standing waves for 4-superlinear Schrödinger-Poisson systems with indefinite potentials. Bull Lond Math Soc. 2017;49(2):226–234.
  • Bartsch T, Liu Z, Weth T. Sign changing solutions of superlinear Schrödinger equations. Comm Partial Differ Equ. 2004;29(1-2):25–42.
  • Chang KC. Infinite-dimensional Morse theory and multiple solution problems. Boston (MA): Birkhäuser; 1993. (Progress in Nonlinear Differential Equations and their Applications; 6).
  • Bartsch T, Li S. Critical point theory for asymptotically quadratic functionals and applications to problems with resonance. Nonlinear Anal. 1997;28(3):419–441.
  • Liu JQ. The Morse index of a saddle point. Systems Sci Math Sci. 1989;2(1):32–39.
  • Wang ZQ. On a superlinear elliptic equation. Ann Inst H Poincaré Anal Non Linéaire. 1991;8(1):43–57.

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