References
- Applebaum D. Lévy processes–from probability to finance quantum groups. Notices Amer Math Soc. 2004;51:1336–1347.
- Molica Bisci G, Rădulescu V, Servadei R Variational methods for nonlocal fractional problems. Cambridge: Cambridge University Press; 2016. (Encyclopedia of mathematics and its applications; 162).
- Zhu X. A perturbation result on positive entire solutions of a semilinear elliptic equation.J Differ Equ. 1991;92:163–178. doi: 10.1016/0022-0396(91)90045-B
- Cao DM, Zhou HS. Multiple positive solutions of nonhomogeneous semilinear elliptic equations in RN. Proc Roy Soc Edinburgh Sect A. 1996;126:443–463. doi: 10.1017/S0308210500022836
- Chen K. Exactly two entire positive solutions for a class of nonhomogeneous elliptic equations. Differ Integral Equ. 2004;17:1–16.
- Chen S, Lin L. Multiple solutions for the nonhomogeneous Kirchhoff equation on RN. Nonlinear Anal RWA. 2013;14:1477–1486. doi: 10.1016/j.nonrwa.2012.10.010
- Chen KJ, Peng CC. Multiplicity and bifurcation of positive solutions for nonhomogeneous semilinear elliptic problems. J Differ Equ. 2007;240:58–91. doi: 10.1016/j.jde.2007.05.023
- Jeanjean L. Two positive solutions for a class of nonhomogeneous elliptic equations. Differ Integral Equ. 1997;10:609–624.
- Li G, Zhou H. The existence of a weak solution of inhomogeneous quasilinear elliptic equation with critical growth conditions. Acta Math Sinica New Ser. 1995;11:146–155. doi: 10.1007/BF02274057
- Wang Z, Zhou H. Positive solutions for a nonhomogeneous elliptic equation on RN without (AR) condition. J Math Anal Appl. 2009;353:470–479. doi: 10.1016/j.jmaa.2008.11.080
- Costa DG, Tehrani H. On a class of asymptotically linear elliptic problems in RN. J Differ Equ. 2001;173:470–494. doi: 10.1006/jdeq.2000.3944
- Fu Y, Zhang X. Multiple solutions for a class of p(x)-Laplacian equations in RN involving the critical exponent. Proc R Soc A. 2010;466:1667–1686. doi: 10.1098/rspa.2009.0463
- Jeanjean L. On the existence of bounded Palais-Smale sequences and applications to a Landesman-Lazer-type set on RN. Proc Roy Soc Edinburgh Sect A. 1999;129:787–809. doi: 10.1017/S0308210500013147
- Liu ZL, Wang Z-Q. Existence of a positive solution of an elliptic equation on RN. Proc Roy Soc Edinburgh Sect A. 2004;134:191–200. doi: 10.1017/S0308210500003152
- Laskin N. Fractional quantum mechanics and Lévy path integrals. Phys Lett A. 2000;268:298–305. doi: 10.1016/S0375-9601(00)00201-2
- Laskin N. Fractional Schrödinger equation. Phys Rev E. 2002;66:056108, 7 pp. doi: 10.1103/PhysRevE.66.056108
- Autuori G, Pucci P. Elliptic problems involving the fractional Laplacian in RN. J Differ Equ. 2013;255:2340–2362. doi: 10.1016/j.jde.2013.06.016
- Fiscella A. Infinitely many solutions for a critical Kirchhoff type problem involving a fractional operator. Differ Integral Equ. 2016;29:513–530.
- Fiscella A, Servadei R, Valdinoci E. Asymptotically linear problems driven by fractional Laplacian operators. Math Meth Appl Sci. 2015;38:3551–3563. doi: 10.1002/mma.3438
- Molica Bisci G, Rădulescu V. Ground state solutions of scalar field fractional for Schrödinger equations. Calc Var Partial Differ Equ. 2015;54:2985–3008. doi: 10.1007/s00526-015-0891-5
- Molica Bisci G, Repovš D. Higher nonlocal problems with bounded potential. J Math Anal Appl. 2014;420:167–176. doi: 10.1016/j.jmaa.2014.05.073
- Pucci P, Xiang M, Zhang B. Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations. Adv Nonlinear Anal. 2016;5:27–55.
- Xiang M, Zhang B, Guo X. Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem. Nonlinear Anal. 2015;120:299–313. doi: 10.1016/j.na.2015.03.015
- Xiang M, Zhang B, Ferrara M. Existence of solutions for Kirchhoff type problem involving the non-local fractional p–Laplacian. J Math Anal Appl. 2015;424:1021–1041. doi: 10.1016/j.jmaa.2014.11.055
- Xiang M, Zhang B, Ferrara M. Multiplicity results for the nonhomogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities. Proc Roy Soc A. 2015;471:1–14. doi: 10.1098/rspa.2015.0034
- Xiang M, Zhang B, Rădulescu V. Existence of solutions for perturbed fractional p-Laplacian equations. J Differ Equ. 2016;260:1392–1413. doi: 10.1016/j.jde.2015.09.028
- Zhang X, Zhang B, Repovš D. Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials. Nonlinear Anal. 2016;142:48–68. doi: 10.1016/j.na.2016.04.012
- Pucci P, Xiang M, Zhang B. Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p–Laplacian in RN. Calc Var Partial Differ Equ. 2015;54:2785–2806. doi: 10.1007/s00526-015-0883-5
- Zhou H. Solutions for a quasilinear elliptic equation with critical Sobolev exponent and perturbations on RN. Differ Integral Equ. 2000;13:595–612.
- Benci V, Cerami G. Positive solutions of some nonlinear elliptic problems in exterior domains. Arch Ration Mech Anal. 1987;99:283–300. doi: 10.1007/BF00282048
- Ekeland I. On the variational principle. J Math Anal Appl. 1974;47:324–353. doi: 10.1016/0022-247X(74)90025-0
- Ambrosetti A, Rabinowiz P. Dual variational methods in critical point theory and applications. J Funct Anal. 1973;14:349–381. doi: 10.1016/0022-1236(73)90051-7
- Felmer P, Quaas A, Tan JG. Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian. Proc Roy Soc Edinburgh Sect A. 2012;142:1237–1262. doi: 10.1017/S0308210511000746
- Badiale M, Citti G. Concentration compactness principle and quasilinear elliptic equations in Rn. Commun Partial Differ Equ. 1991;16:1795–1818. doi: 10.1080/03605309108820823
- 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
- Chabrowski J. Variational methods for potential operator equations. Berlin: de Gruyter; 1997.
- Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc. 1983;88:486–490. doi: 10.2307/2044999
- Willem M. Minimax theorems. Boston: Birkhäuser; 1996.