[1]

C. O. Alves and O. H. Miyagaki,
Existence and concentration of solution for a class of fractional elliptic equation in ${\mathbb{R}}^{N}$ via penalization method,
Calc. Var. Partial Differential Equations 55 (2016), no. 3, Article ID 47.
Google Scholar

[2]

C. O. Alves and M. A. S. Souto,
Existence of solutions for a class of nonlinear Schrödinger equations with potential vanishing at infinity,
J. Differential Equations 254 (2013), no. 4, 1977–1991.
CrossrefGoogle Scholar

[3]

C. O. Alves and M. A. S. Souto,
Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains,
Z. Angew. Math. Phys. 65 (2014), no. 6, 1153–1166.
CrossrefGoogle Scholar

[4]

A. Ambrosetti, V. Felli and A. Malchiodi,
Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity,
J. Eur. Math. Soc. (JEMS) 7 (2005), no. 1, 117–144.
Google Scholar

[5]

A. Ambrosetti and Z.-Q. Wang,
Nonlinear Schrödinger equations with vanishing and decaying potentials,
Differential Integral Equations 18 (2005), no. 12, 1321–1332.
Google Scholar

[6]

V. Ambrosio,
Multiplicity and concentration results for a fractional Choquard equation via penalization method,
Potential Anal. (2017), 10.1007/s11118-017-9673-3.
Google Scholar

[7]

V. Ambrosio,
Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method,
Ann. Mat. Pura Appl. (4) 196 (2017), no. 6, 2043–2062.
CrossrefGoogle Scholar

[8]

V. Ambrosio,
Mountain pass solutions for the fractional Berestycki–Lions problem,
Adv. Differential Equations 23 (2018), no. 5–6, 455–488.
Google Scholar

[9]

V. Ambrosio and G. M. Figueiredo,
Ground state solutions for a fractional Schrödinger equation with critical growth,
Asymptot. Anal. 105 (2017), no. 3–4, 159–191.
CrossrefGoogle Scholar

[10]

V. Ambrosio and H. Hajaiej,
Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in ${\mathbb{R}}^{\mathbb{N}}$,
J. Dynam. Differential Equations (2017), 10.1007/s10884-017-9590-6.
Google Scholar

[11]

V. Ambrosio and T. Isernia,
A multiplicity result for a fractional Kirchhoff equation in ${\mathbb{R}}^{\mathbb{N}}$ with a general nonlinearity,
Commun. Contemp. Math. (2016), 10.1142/S0219199717500547.
Google Scholar

[12]

V. Ambrosio and T. Isernia,
Sign-changing solutions for a class of Schrödinger equations with vanishing potentials,
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 29 (2018), no. 1, 127–152.
CrossrefGoogle Scholar

[13]

G. Autuori and P. Pucci,
Elliptic problems involving the fractional Laplacian in ${\mathbb{R}}^{\mathbb{N}}$,
J. Differential Equations 255 (2013), no. 8, 2340–2362.
Google Scholar

[14]

S. Barile and G. M. Figueiredo,
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. 427 (2015), no. 2, 1205–1233.
Google Scholar

[15]

T. Bartsch, Z. Liu and T. Weth,
Sign changing solutions of superlinear Schrödinger equations,
Comm. Partial Differential Equations 29 (2004), no. 1–2, 25–42.
Google Scholar

[16]

T. Bartsch, A. Pankov and Z.-Q. Wang,
Nonlinear Schrödinger equations with steep potential well,
Commun. Contemp. Math. 3 (2001), no. 4, 549–569.
CrossrefGoogle Scholar

[17]

T. Bartsch and T. Weth,
Three nodal solutions of singularly perturbed elliptic equations on domains without topology,
Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 3, 259–281.
CrossrefGoogle Scholar

[18]

T. Bartsch, T. Weth and M. Willem,
Partial symmetry of least energy nodal solutions to some variational problems,
J. Anal. Math. 96 (2005), 1–18.
CrossrefGoogle Scholar

[19]

V. Benci, C. R. Grisanti and A. M. Micheletti,
Existence of solutions for the nonlinear Schrödinger equation with $V(\mathrm{\infty})=0$,
Contributions to Nonlinear Analysis,
Progr. Nonlinear Differential Equations Appl. 66,
Birkhäuser, Basel (2006), 53–65.
Google Scholar

[20]

H. Berestycki and P.-L. Lions,
Nonlinear scalar field equations. I. Existence of a ground state,
Arch. Ration. Mech. Anal. 82 (1983), no. 4, 313–345.
CrossrefGoogle Scholar

[21]

G. Molica Bisci and V. D. Rădulescu,
Ground state solutions of scalar field fractional Schrödinger equations,
Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2985–3008.
CrossrefGoogle Scholar

[22]

D. Bonheure and J. Van Schaftingen,
Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity,
Ann. Mat. Pura Appl. (4) 189 (2010), no. 2, 273–301.
CrossrefGoogle Scholar

[23]

C. Bucur and E. Valdinoci,
Nonlocal Diffusion and Applications,
Lect. Notes Unione Mat. Ital. 20,
Unione Matematica Italiana, Bologna, 2016.
Google Scholar

[24]

X. Cabré and J. Solà-Morales,
Layer solutions in a half-space for boundary reactions,
Comm. Pure Appl. Math. 58 (2005), no. 12, 1678–1732.
CrossrefGoogle Scholar

[25]

L. Caffarelli, J.-M. Roquejoffre and O. Savin,
Nonlocal minimal surfaces,
Comm. Pure Appl. Math. 63 (2010), no. 9, 1111–1144.
Google Scholar

[26]

L. Caffarelli and L. Silvestre,
An extension problem related to the fractional Laplacian,
Comm. Partial Differential Equations 32 (2007), no. 7–9, 1245–1260.
CrossrefGoogle Scholar

[27]

L. A. Caffarelli, S. Salsa and L. Silvestre,
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian,
Invent. Math. 171 (2008), no. 2, 425–461.
CrossrefGoogle Scholar

[28]

A. Castro, J. Cossio and J. M. Neuberger,
A sign-changing solution for a superlinear Dirichlet problem,
Rocky Mountain J. Math. 27 (1997), no. 4, 1041–1053.
CrossrefGoogle Scholar

[29]

J. Dávila, M. del Pino, S. Dipierro and E. Valdinoci,
Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum,
Anal. PDE 8 (2015), no. 5, 1165–1235.
CrossrefGoogle Scholar

[30]

J. Dávila, M. del Pino and J. Wei,
Concentrating standing waves for the fractional nonlinear Schrödinger equation,
J. Differential Equations 256 (2014), no. 2, 858–892.
CrossrefGoogle Scholar

[31]

E. Di Nezza, G. Palatucci and E. Valdinoci,
Hitchhiker’s guide to the fractional Sobolev spaces,
Bull. Sci. Math. 136 (2012), no. 5, 521–573.
CrossrefGoogle Scholar

[32]

S. Dipierro, M. Medina and E. Valdinoci,
Fractional elliptic problems with critical growth in the whole of ${\mathbb{R}}^{\mathbb{N}}$,
Appunti. Sc. Norm. Super. Pisa (N. S.) 15,
Edizioni della Normale, Pisa, 2017.
Google Scholar

[33]

S. Dipierro, G. Palatucci and E. Valdinoci,
Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian,
Mat. (Catania) 68 (2013), no. 1, 201–216.
Google Scholar

[34]

P. Felmer, A. Quaas and J. Tan,
Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian,
Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 6, 1237–1262.
CrossrefGoogle Scholar

[35]

G. M. Figueiredo and J. R. Santos Júnior,
Existence of a least energy nodal solution for a Schrödinger–Kirchhoff equation with potential vanishing at infinity,
J. Math. Phys. 56 (2015), no. 5, Article ID 051506.
Google Scholar

[36]

G. M. Figueiredo and G. Siciliano,
A multiplicity result via Ljusternick–Schnirelmann category and Morse theory for a fractional Schrödinger equation in ${\mathbb{R}}^{N}$,
NoDEA Nonlinear Differential Equations Appl. 23 (2016), no. 2, Article ID 12.
Google Scholar

[37]

A. Fiscella, P. Pucci and S. Saldi,
Existence of entire solutions for Schrödinger–Hardy systems involving two fractional operators,
Nonlinear Anal. 158 (2017), 109–131.
CrossrefGoogle Scholar

[38]

R. L. Frank, E. Lenzmann and L. Silvestre,
Uniqueness of radial solutions for the fractional Laplacian,
Comm. Pure Appl. Math. 69 (2016), no. 9, 1671–1726.
CrossrefGoogle Scholar

[39]

F. Gazzola and V. Rădulescu,
A nonsmooth critical point theory approach to some nonlinear elliptic equations in ${\mathbb{R}}^{n}$,
Differential Integral Equations 13 (2000), no. 1–3, 47–60.
Google Scholar

[40]

T. Isernia,
Positive solution for nonhomogeneous sublinear fractional equations in ${\mathbb{R}}^{N}$,
Complex Var. Elliptic Equ. 63 (2018), no. 5,689–714.
Google Scholar

[41]

T. Kuusi, G. Mingione and Y. Sire,
Nonlocal equations with measure data,
Comm. Math. Phys. 337 (2015), no. 3, 1317–1368.
CrossrefGoogle Scholar

[42]

N. Laskin,
Fractional quantum mechanics and Lévy path integrals,
Phys. Lett. A 268 (2000), no. 4–6, 298–305.
CrossrefGoogle Scholar

[43]

N. Laskin,
Fractional Schrödinger equation,
Phys. Rev. E (3) 66 (2002), no. 5, Article ID 056108.
Google Scholar

[44]

C. Miranda,
Un’osservazione su un teorema di Brouwer,
Boll. Un. Mat. Ital. (2) 3 (1940), 5–7.
Google Scholar

[45]

G. Molica Bisci, V. D. Radulescu and R. Servadei,
Variational Methods for Nonlocal Fractional Problems,
Encyclopedia Math. Appl. 162,
Cambridge University Press, Cambridge, 2016.
Google Scholar

[46]

P. Pucci and S. Saldi,
Multiple solutions for an eigenvalue problem involving non-local elliptic *p*-Laplacian operators,
Geometric Methods in PDE’s,
Springer INdAM Ser. 13,
Springer, Cham (2015), 159–176.
Google Scholar

[47]

P. Pucci and S. Saldi,
Critical stationary Kirchhoff equations in ${\mathbb{R}}^{N}$ involving nonlocal operators,
Rev. Mat. Iberoam. 32 (2016), no. 1, 1–22.
Google Scholar

[48]

P. H. Rabinowitz,
Minimax Methods in Critical Point Theory with Applications to Differential Equations,
CBMS Reg. Conf. Ser. Math. 65,
American Mathematical Society, Providence, 1986.
Google Scholar

[49]

P. H. Rabinowitz,
On a class of nonlinear Schrödinger equations,
Z. Angew. Math. Phys. 43 (1992), no. 2, 270–291.
CrossrefGoogle Scholar

[50]

S. Secchi,
Ground state solutions for nonlinear fractional Schrödinger equations in ${\mathbb{R}}^{N}$,
J. Math. Phys. 54 (2013), no. 3, Article ID 031501.
Google Scholar

[51]

W. A. Strauss,
Existence of solitary waves in higher dimensions,
Comm. Math. Phys. 55 (1977), no. 2, 149–162.
CrossrefGoogle Scholar

[52]

A. Szulkin and T. Weth,
The method of Nehari manifold,
Handbook of Nonconvex Analysis and Applications,
International Press, Somerville (2010), 597–632.
Google Scholar

[53]

M. Willem,
Minimax Theorems,
Progr. Nonlinear Differential Equations Appl. 24,
Birkhäuser, Boston, 1996.
Google Scholar

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