## REFERENCES

[1] X. Chang, Z. Wang, Ground state of scalar field equations involving a fractional Laplacian

with general nonlinearity, Nonlinearity, 26 (2013) 479-494.

[2] X. Chang, Ground state solutions of asymptotically linear fractional Schr¨odinger equations, J.

Math. Phys. 54, 061504 (2013).

[3] Y. Wei, X. Su, Multiplicity of solutions for non-local elliptic equations driven by the fractional

Laplacian, Calc. Var. 52 (2015) 95-124.

[4] Z. Zhang, R. Yuan, Variational approach to solutions for a class of fractional Hamiltonian

systems, Math. Methods Appl. Sci. 37 (2014) 1873-1883.

[5] S. Secchi, Ground state solutions for nonlinear fractional Schr¨odinger equations in R

N , J.

Math. Phys. 54, 031501 (2013).

262 J. XU, W. DONG, AND D. O’REGAN

[6] X. Cabr´e, Y. Sire, Nonlinear equations for fractional Laplacians, I: Regularity, maximum

principles, and Hamiltonian estimates, Ann. Inst. H. Poincar´e Anal. Non Lin´eaire 31 (2014)

23-53.

[7] Y. Hua, X. Yu, On the ground state solution for a critical fractional Laplacian equation,

Nonlinear Anal. 87 (2013) 116-125.

[8] B. Barrios, E. Colorado, A. de Pablo, U. S´anchez, On some critical problems for the fractional

Laplacian operator, J. Differential Equations 252 (2012) 6133-6162.

[9] G. Autuori, P. Pucci, Elliptic problems involving the fractional Laplacian in R

N , J. Differential

Equations 255 (2013) 2340-2362.

[10] S. Dipierro, A. Pinamonti, A geometric inequality and a symmetry result for elliptic systems

involving the fractional Laplacian, J. Differential Equations 255 (2013) 85-119.

[11] K. Teng, Multiple solutions for a class of fractional Schr¨odinger equations in R

N , Nonlinear

Anal. Real World Appl. 21 (2015) 76-86.

[12] T. Gou, H. Sun, Solutions of nonlinear Schr¨odinger equation with fractional Laplacian without

the Ambrosetti-Rabinowitz condition, Appl. Math. Comput. 257 (2015) 409-416.

[13] J. Xu, Z. Wei, W. Dong, Existence of weak solutions for a fractional Schr¨odinger equation,

Commun. Nonlinear Sci. Numer. Simul. 22 (2015) 1215-1222.

[14] M. Struwe, Variational Methods, Applications to Nonlinear Partial Differential Equations and

Hamiltonian Systems, 3rd ed., Springer-Verlag, New York, 2000.

[15] A. Ambrosetti, P. Rabinowitz, Dual variational methods in critical point theorey and applications,

J. Funct. Anal. 14 (1973) 349-381.

[16] M. Willem, Minimax Theorems, Birkh¨aser, Boston, 1996.

[17] Y. Ye, C. Tang, Multiple solutions for Kirchhoff-type equations in R

N , J. Math. Phys. 54,

081508 (2013).

[18] L. Duan, L. Huang, Infinitely many solutions for sublinear Schr¨odinger-Kirchhoff-Type equations

with general potentials, Results. Math. 66 (2014) 181-197.