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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 11
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Research Article

Existence and multiplicity of solutions for perturbed fractional p-Laplacian equations with critical nonlinearity in N

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Pages 2960-2977 | Received 02 Nov 2021, Accepted 10 Feb 2022, Published online: 03 Mar 2022

References

  • Nezza ED, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573.
  • Caffarelli LA. Nonlocal equations, drifts and games, nonlinear partial differential equations. Abel Symp. 2012;7:37–52.
  • Laskin N. Fractional quantum mechanics and Levy path integrals. Phys Lett A. 2000;268:298–305.
  • Laskin N. Fractional Schrödinger equation. Phys Rev E. 2002;66:056108.
  • Felmer P, Quass A, Tan JG. Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian. Proc R Soc Edinb. 2012;A142:1237–1262.
  • Cabre X, Tan JG. Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv Math. 2010;224:2052–2093.
  • Autuori G, Pucci P. Elliptic problems involving the fractional Laplacian in RN. J Differ Equ. 2013;255:2340–2362.
  • Teng KM. Multiple solutions for a class of fractional Schrödinger equations in RN. Nonlinear Anal-Real World Appl. 2015;21:76–86.
  • Shen LJ. Multiplicity and concentration results for fractional Schrödinger system with steep potential wells. J Math Anal Appl. 2019;475:1385–1403.
  • Papageorgiou NS, Scapellato A. Nonlinear Robin problems with general potential and crossing reaction. Rend Lincei-Mat Appl. 2019;30:1–29.
  • Iannizzotto A, Squassina M. Weyl-type laws for fractional p-eigenvalue problems. Asymptot Anal. 2014;88:233–245.
  • Perera K, Squassina M, Yang Y. A note on the dancer-Fuík spectra of the fractional p-Laplacian and Laplacian operators. Adv Nonlinear Anal. 2015;4:13–23.
  • Castro AD, Kuusi T, Palatucci G. Local behavior of fractional p-minimizers. Ann Inst H Poincaré Anal Non Linéaire. 2016;33:1279–1299.
  • Chen WJ, Mosconi S, Squassina M. Nonlocal problems with critical Hardy nonlinearity. J Funct Anal. 2018;275:3065–3114.
  • Chen CS, Bao JF, Song HX. Multiple solutions for a class of fractional (p,q)-Laplacian system in RN. J Math Phys. 2018;59:031505.
  • Li Q, Yang ZD. Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in RN. Complex Var Elliptic Equ. 2016;61:969–983.
  • Ambrosio V, Isernia T. Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional p-Laplacian. Discrete Contin Dyn Syst. 2018;38:5835–5881.
  • Lou QJ, Luo H. Multiplicity and concentration of positive solutions for fractional p-Laplacian problem involving concave-convex nonlinearity. Nonlinear Anal-Real Word Appl. 2018;42:387–408.
  • Truong LX. The Nehari manifold for fractional p-Laplacian equation with logarithmic nonlinearity on whole space. Comput Math Appl. 2019;78:3931–3940.
  • Pucci P, Temperini L. Existence for fractional (p,q) systems with critical and Hardy terms in RN. Nonlinear Anal. 2021;211:112477.
  • Chen WJ, Gui YY. Multiplicity of solutions for fractional p&q-Laplacian system involving critical concave-convex nonlinearities. Appl Math Lett. 2019;96:81–88.
  • Wang XS, Yang ZD. Nonexistence of positive solutions for an indefinite fractional p-Laplacian. Nonlinear Anal. 2020;195:111740.
  • Cheng BT, Tang XH. New existence of solutions for the fractional p-Laplacian equations with sign-changing potential and nonlinearity. Mediterr J Math. 2016;13:3373–3387.
  • Xiang MQ, Zhang BL, Radulescu VD. Existence of solutions for perturbed fractional p-Laplacian equations. J Differ Equ. 2016;260:1392–1413.
  • Torres C. Existence and symmetry result for fractional p-Laplacian in RN. Commun Pure Appl Anal. 2017;16:99–113.
  • Ambrosio V. Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method. Annali Di Mathematica Pura Ed Applicata. 2017;196:1–20.
  • Shang XD, Zhang JH. Concentrating solutions of nonlinear fractional Schrödinger equation with potentials. J Differ Equ. 2015;258:1106–1128.
  • Alves CO, Ambrosio V. A multiplicity result for a nonlinear fractional Schrödinger equation in RN without the Ambrosetti-Rabinowitz condition. J Math Anal Appl. 2018;466:498–522.
  • He XM, Zou WM. Existence and concentration result for the fractional Schrödinger equations with critical nonlinearity. Calculus Var Partial Differ Equ. 2016;55:91.
  • Figueiredo GM, Siciliano G. A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in RN. Nonlinear Differ Equ Appl. 2016;23:1–22.
  • Alves CO, Miyagaki OH. Existence and concentration of solution for a class of fractional elliptic equation in RN via penalization method. Calculus Var Partial Differ Equ. 2016;55:47.
  • Alves CO, Souto MAS. On existence and concentration behavior of ground state solutions for a class of problems with critical growth. Commun Pure Appl Anal. 2002;3:417–431.
  • Pino MD, Felmer PL. Local mountain pass for semilinear elliptic problems in unbounded domains. Calculus Var Partial Differ Equ. 1996;4:121–137.
  • Ambrosetti A, Badiale M, Cingolani S. Semiclassical states of nonlinear Schrödinger equations. Arch Ration Mech Anal. 1997;140:285–300.
  • Jeanjean L, Tanaka K. Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities. Calculus Var Partial Differ Equ. 2004;21:287–318.
  • Ding YH, Lin FH. Solutions of perturbed Schrödinger equations with critical nonlinearity. Calculus Var Partial Differ Equ. 2007;30:231–249.
  • Yang MB, Ding YH. Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in RN. Annali Di Matematica. 2013;192:783–804.
  • Li Q, Yang ZD. Existence of solutions for a perturbed p-Laplacian system with critical exponent in RN. Appl Anal. 2017;96:1885–1905.
  • Brézis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc. 1983;88:486–490.
  • Su J, Wang ZQ, Willem M. Weighted Sobolev embedding with unbounded and decaying radial potentials. J Differ Equ. 2007;238:201–219.
  • Benci V. On critical point theory of indefinite functionals in the presence of symmetries. Trans Am Math Soc. 1982;274:533–572.

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