[1] Ambrosetti A, Felli V, Malchiodi A. Ground states of nonlinear Schr¨odinger equations with potentials
vanishing at infinity. J Eur Math Soc, 2005, 7: 117–144

[2] Ambrosetti A, Malchiodi A. Perturbation Methods and Semilinear Elliptic Problems on R^N . Progress in
Mathematics, Vol 240. Basel: Birkh¨auser, 2006

[3] Ambrosetti A, Malchiodi A, Ruiz D. Bound states of nonlinear Schr¨odinger equations with potentials
vanishing at infinity. J Anal Math, 2006, 98: 317–348

[4] Ambrosetti A, Wang Z -Q. Nonlinear Schr¨odinger equations with vanishing and decaying potentials. Dif-
ferential and Integral Equations, 2005, 18: 1321–1332

[5] Astarita G, Marrucci G. Principles of Non-Newtonian Fluid Mechanics. McGraw-Hill, 1974

[6] Ba N, Deng Y, Peng S. Multi-peak bound states for Schr¨odinger equations with compactly supported or
unbounded potentials. Ann Inst H Poincar′e Anal Non Lin′eaire, 2010, 27: 1205–1226

[7] Benci V, D’Avenia P, Fortunato D, Pisani L. Solitons in several space dimensions: Derrick’s problem and
infinitely many solutions. Arch Rational Mech Anal, 2000, 154: 297–324

[8] Berestycki H,LionsP L.Nonlinear scalarfield equations I, II. ArchRational Mech Anal, 1983, 82: 313–345,
347–375

[9] Berezin F A, Shubin M A. The Schr¨odinger Equation. Dordrecht: Kluwer Acad Publ, 1991

[10] Bonheure D, Van Schaftingen J. Bound state solutions for a class of nonlinear Schr¨odinger equations. Rev Mat Iberoamericana, 2008, 24: 297–351

[11] Bonheure D, Van Schaftingen J. Groundstates for the nonlinear Schr¨odinger equation with potential van-
ishing at infinity. Ann Mat Pura Appl, 2010, 189: 273–301

[12] Cao D, Peng S. Semi-classical bound states for Schr¨odinger equations with potentials vanishing or un-
bounded at infinity. Comm Partial Di?er Equ, 2009, 34: 1566–1591

[13] Coleman S, Glazer V, Martin A. Action minima among solutions to a class of Euclidean scalar field equations. Comm Math Phys, 1978, 58: 211–221

[14] D′iaz J I. Nonlinear Partial Differential Equations and Free Boundaries, Vol I: Elliptic Equations. Pitman
Research Notes in Mathematics, Vol 106. Boston, MA: Pitman, 1985

[15] Fei M, Yin H. Existence and concentration of bound states of nonlinear Schr¨odinger equations with com-
pactly supported and competing potentials. Pacific J Math, 2010, 244: 261–296

[16] Fleckinger J, Harrell II E, de Th′elin F. Boundary behavior and estimates for solutions of equations con-
taining the p-Laplacian. Electr J Di? Eq, 1999, 38: 1–19

[17] Floer A, Weinstein A. Nonspreading wave packets for the cubic Schr¨odinger equation with a bounded
potential. J Funct Anal, 1986, 69: 397–408

[18] Garcia Azorero J P, Peral Alonso I. Hardy inequalities and some critcal elliptic and parabolic problems.
J Di?er Equ, 1998, 144: 441–476

[19] Kachanov L M. Foundations of the Theory of Plasticity. North Holland, 1971

[20] Liu C, Wang Z, Zhou H -S. Asymptotically linear Schr¨odinger equation with potential vanishing at infinity.
J Di?er Equ, 2008, 245: 201–222

[21] Liskevich V,Lyakhova S,MorozV.Positivesolutionsto nonlinear p-Laplaceequations withHardypotential in exterior domains. J Differ Equ, 2007, 232: 212–252

[22] Lyberopoulos A N. Quasilinear scalar field equations with competing potentials. J Di?er Equ, 2011, 251:
3625–3657

[23] Moroz V, Van Schaftingen J. Semiclassical stationary states for nonlinear Schr¨odinger equations with fast
decaying potentials. Calc Var Partial Di?er Equ, 2010, 37: 1–27

[24] Strauss W. Existence of solitary waves in higher dimensions. Comm Math Phys, 1977, 55: 149–162

[25] Sulem C, Sulem P -L. The Nonlinear Schr¨odinger Equation: Self-Focusing and Wave Collapse. Applied
Mathematical Sciences, Vol 139. New York: Springer-Verlag, 1999

[26] Yin H, Zhang P. Bound states of nonlinear Schr¨odinger equations with potentials tending to zero at infinity.
J Differ Equ, 2009, 247: 618–647