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Original Articles

Existence of solutions for critical fractional p&q-Laplacian system

Pages 626-641 | Received 26 Mar 2019, Accepted 23 Feb 2020, Published online: 11 Mar 2020

References

  • Di Castro A, Kuusi T, Palatucci G. Local behavior of fractional p-minimizers. Ann Inst Henri Poincaré Anal Non Linéaire. 2016;33(5):1279–1299. doi: 10.1016/j.anihpc.2015.04.003
  • Chen W, Deng S. The Nehari manifold for non-local elliptic operators involving concave-convex nonlinearities. Z Angew Math Phys. 2015;66:1387–1400. doi: 10.1007/s00033-014-0486-6
  • Chen W, Deng S. The Nehari manifold for a fractional p-Laplacian system involving concave-convex nonlinearities. Nonlinear Anal Ser B: Real World Appl. 2016;27:80–92. doi: 10.1016/j.nonrwa.2015.07.009
  • Cotsiolis A, Tavoularis N. Best constants for Sobolev inequalities for higher order fractional derivatives. J Math Anal Appl. 2004;295:225–236. doi: 10.1016/j.jmaa.2004.03.034
  • Goyal S, Sreenadh K. Nehari manifold for non-local elliptic operator with concave-convex non-linearities and sign-changing weight function. Proc Indian Acad Sci (Math Sci). 2015;125(4):545–558. doi: 10.1007/s12044-015-0244-5
  • Goyal S, Sreenadh K. Existence of multiple solutions of p-fractional Laplace operator with sign-changing weight function. Adv Nonlinear Anal. 2015;4(1):37–58.
  • Lehrer R, Maia LA, Squassina M. On fractional p-Laplacian problems with weight. Differ Integral Equ. 2015;28(1/2):15–28.
  • Iannizzotto A, Liu S, Perera K, et al. Existence results for fractional p-Laplacian problems via Morse theory. Adv Calc Var. 2016;9(2):101–125. doi: 10.1515/acv-2014-0024
  • Perera K, Squassina M, Yang Y. Bifurcation results for critical growth fractional p-Laplacian problems. Math Nachr. 2016;289:332–342. doi: 10.1002/mana.201400259
  • Servadei R, Valdinoci E. Mountain pass solutions for non-local elliptic operators. J Math Anal Appl. 2012;389:887–898. doi: 10.1016/j.jmaa.2011.12.032
  • Barile S, Figueiredo G. Existence of least energy positive, negative and nodal solutions for a class of p&q-problems with potentials vanishing at infinity. J Math Anal Appl. 2015;427(2):1205–1233. doi: 10.1016/j.jmaa.2015.02.086
  • Candito P, Marano S, Perera K. On a class of critical (p,q)-Laplacian problems. Nonlinear Differ Equ Appl. 2015;22(6):1959–1972. doi: 10.1007/s00030-015-0353-y
  • Hu S, Papageorgiou N. Positive solutions for resonant (p,q)-equations with concave terms. Commun Pure Appl Anal. 2018;17(6):2639–2656. doi: 10.3934/cpaa.2018125
  • Li G. The existence of a nontrivial solution to the p&q-Laplacian problem with nonlinearity asymptotic to up−1 at infinity in RN. Nonlinear Anal. 2008;68:1100–1119. doi: 10.1016/j.na.2006.12.008
  • Li G, Zhang G. Multiple solutions for the p&q-Laplacian problem with critical exponent. Acta Math Sci. 2009;29B(4):903–918.
  • Marano S, Mosconi S. Some recent results on the Dirichlet problem for (p,q)-Laplace equations. Discrete Contin Dyn Syst. 2018;11(2):279–291. doi: 10.3934/dcdss.2018015
  • Marano S, Mosconi S, Papageorgiou N. On a (p,q)-Laplacian problem with parametric concave term and asymmetric perturbation. Atti Accad Naz Lincei Rend Lincei Mat Appl. 2018;29(1):109–125. doi: 10.4171/RLM/796
  • Yin H. Existence of multiple positive solutions for a p–q-Laplacian system with critical nonlinearities. J Math Anal Appl. 2013;403:200–214. doi: 10.1016/j.jmaa.2013.02.032
  • Yin H, Yang Z. Existence of positive solutions for a class of quasilinear elliptic system with concave-convex nonlinearities. J Appl Math Inform. 2011;29(34):921–936.
  • Fu Y, Li H, Pucci P. Existence of nonnegative solutions for a class of systems involving fractional (p,q)-Laplacian operators. Chin Ann Math Ser B. 2018;39(2):357–372. doi: 10.1007/s11401-018-1069-1
  • Xiang M, Zhang B, Wei Z. Existence of solutions to a class of quasilinear Schrödinger systems involving the fractional p-Laplacian. Electron J Qual Theory Differ Equ. 2016;107:1–15. doi: 10.14232/ejqtde.2016.1.107
  • Xiang M, Zhang B, Rădulescu V. Multiplicity of solutions for a class of quasilinear Kirchhoff system involving the fractional p-Laplacian. Nonlinearity. 2016;29:3186–3205. doi: 10.1088/0951-7715/29/10/3186
  • Bhakta M, Mukherjee D. Multiplicity results for (p,q) fractional elliptic equations involving critical nonlinearities. Adv Differ Equ. 2019;24(3–4);185–228.
  • Alves CO, Ambrosio V, Isernia T. Existence, multiplicity and concentration for a class of fractional p&q Laplacian problems in RN. Commun Pure Appl Anal. 2019;18(4):2009–2045. doi: 10.3934/cpaa.2019091
  • Ambrosio V. Fractional p&q Laplacian problems in RN with critical growth. arxiv:1801.10449.
  • Ambrosio V, Isernia T. On a fractional p&q Laplacian problem with critical Sobolev-Hardy exponents. Mediterr J Math. 2018;15(6):17. doi: 10.1007/s00009-018-1259-9
  • Chen C, Bao J. Existence, nonexistence, and multiplicity of solutions for the fractional p&q-Laplacian equation in RN. Bound Value Prob. 2016;2016(1):153. doi: 10.1186/s13661-016-0661-0
  • Chen W, Gui Y. Multiplicity of solutions for fractional p&q-Laplacian system involving critical concave-convex nonlinearities. Appl Math Lett. 2019;96:81–88. doi: 10.1016/j.aml.2019.04.021
  • Goel D, Kumar D, Sreenadh K. Regularity and multiplicity results for fractional (p,q)-Laplacian equations. arxiv: 1902.00395.
  • Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573. doi: 10.1016/j.bulsci.2011.12.004
  • Chen W, Squassina M. Critical nonlocal systems with concave-convex towers. Adv Nonlinear Stud. 2016;16(4):821–842. doi: 10.1515/ans-2015-5055
  • Mosconi S, Perera K, Squassina M, et al. The Brezis-Nirenberg problem for the fractional p-Laplacian. Calc Var Partial Differ Equ. 2016;55:55–105. doi: 10.1007/s00526-016-1035-2
  • Brasco L, Mosconi S, Squassina M. Optimal decay of extremal functions for the fractional Sobolev inequality. Calc Var Partial Differ Equ. 2016;55:1–32. doi: 10.1007/s00526-016-0958-y
  • Brezis H. Analyse fonctionelle. Théorie et applications. Paris: Masson; 1983.
  • Brasco L, Squassina M, Yang Y. Global compactness results for nonlocal problems. Discrete Contin Dyn Syst Ser S. 2018;11(3):391–424.
  • Ambrosetti A, Rabinowitz PH. Dual variational methods in critical point theory and application. J Funct Anal. 1973;14:349–381. doi: 10.1016/0022-1236(73)90051-7

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