References
- Deng Y, Peng S, Yan S. Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth. J Differ Equ. 2015;258:115–147.
- Shen Y, Wang Y. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Anal. 2013;80:194–201.
- Deng Y, Huang W. Ground state solutions for generalized quasilinear Schrödinger equations without (AR) condition. J Math Anal Appl. 2017;456:927–945.
- Deng Y, Huang W. Positive ground state solutions for a quasilinear elliptic equation with critical exponent. Discrete Contin Dyn Syst. 2017;37:4213–4230.
- Ding Y, Lin F. Solutions of perturbed Schrödinger equations with critical nonlinearity. Calc Var Partial Differ Equ. 2007;30:231–249.
- Ding Y, Liu X. Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities. Manuscripta Math. 2013;140:51–82.
- He X, Qian A, Zou W. Existence and concentration of positive solutions for quasilinear Schrödinger equations with critical growth. Nonlinearity. 2013;26:3137–3168.
- He Y, Li G. Concentration soliton solutions for quasilinear Schröinger equations involving critical Sobolev exponents. Discrete Contin Dyn Syst. 2016;36:731–762.
- Li F, Zhu X, Liang Z. Multiple solutions to a class of generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation. J Math Anal Appl. 2016;443:11–38.
- Li Z, Zhang Y. Solutions for a class of quasilinear Schrödinger equations with critical Sobolev exponents. J Math Phys. 2017;58:021501.
- Shen L. Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems. Boundary Value Probl. 2018;2018:44.
- Zhu X, Li F, Liang Z. Existence of ground state solutions to a generalized quasilinear Schrödinger–Maxwell system. J Math Phys. 2016;57:101505.
- Kirchhoff G. Mechanik. Leipzig: Teubner; 1883.
- Lions JL. On some questions in boundary value problems of mathematical physics. In: Contemporary Developments in Continuum Mechanics and Partial Differential Equations, Proceedings of International Symposium, Inst. Mat. Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977. North-Holland, Amsterdam; 1978. p. 284–346. (North-Holland Math. Stud.; vol. 30).
- Chen J, Tang X, Cheng B. Existence and nonexistence of positive solutions for a class of generalized quasilinear Schrödinger equations involving a Kirchhoff-type perturbation with critical Sobolev exponent. J Math Phys. 2018;59:021505.
- Deng Y, Peng S, Shuai W. Existence and asympototic behavior of nodal solutions for the Kirchhoff type problems in R3. J Funct Anal. 2015;269:3500–3527.
- Deng Y, Shuai W. Sign-changing multi-bump solutions for Kirchhoff-type equations in R3. Discrete Contin Dyn Syst. 2018;38:3139–3168.
- Figueiredo GM, Ikoma N, Júnior JR. Existence and concentration result for the Kirchhoff type equations with general nonlinearities. Arch Rational Mech Anal. 2014;213:931–979.
- Guo Z. Ground states for Kirchhoff equations without compact condition. J Differ Equ. 2015;259:2884–2902.
- He X, Zou W. Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3. J Differ Equ. 2012;2:1813–1834.
- He Y, Li G. Standing waves for a class of Kirchhoff type problems in R3 involving critical Sobolev exponents. Calc Var Partial Differ Equ. 2015;54:3067–3106.
- He Y. Concentrating bounded states for a class of singularly perturbed Kirchhoff type equations with a general nonlinearity. J Differ Equ. 2016;261:6178–6220.
- Li G, Ye H. Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R3. J Differ Equ. 2014;257:566–600.
- Shuai W. Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains. J Differ Equ. 2015;259:1256–1274.
- Wang J, Tian L, Xu J, et al. Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth. J Differ Equ. 2012;253:2314–2351.
- Ye H. Positive high energy solution for Kirchhoff equation in R3 with superlinear nonlinearities via Nehair–Pohozaev manifold. Discrete Contin Dyn Syst. 2015;35:3857–3877.
- Willem M. Minimax theorems. Boston: Birkhäuser; 1996.
- Berestycki H, Lions PL. Nonlinear scalar field equations I, existence of a ground state. Arch Ration Mech Anal. 1983;82:313–345.
- Jeanjean L. On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer type problem set on RN. Proc Roy Soc Edinburgh Sect A. 1999;129:787–809.
- Lions PL. The concentration-compactness principle in the calculus of variation. The locally compact case. Part I. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:109–145.
- Lions PL. The concentration-compactness principle in the calculus of variation. The locally compact case. Part II. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:223–283.
- Jeanjean L. Existence of solutions with prescribed norm for semilinear elliptic equations. Nonlinear Anal Theory Methods Appl. 1997;28:1633–1659.
- Rabinowitz PH. On a class of nonlinear Schrödinger equations. Z Angew Math Phys. 1992;43:270–291.
- Ekeland I. Nonconvex minimization problems. Bull Amer Math Soc. 1979;1:443–473.
- Chabrowski J. Weak convergence methods for semilinear elliptic equations. River Edge (NJ): World Scientific; 1999.
- Brézis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc. 1983;88:486–490.
- Li G, Luo P, Peng S, et al. Uniqueness and nondegeneracy of positive solutions to Kirchhoff equations and its applications in singular perturbation problems. arXiv:1703.05459.
- Bartsch T, Weth T. Three nodal solutions of singularly perturbed elliptic equations on domains with topology. Ann I H Poincare-AN. 2005;22:259–281.
- Cerami G, Passaseo D. The effect of concentrating potentials in some singularly perturbed problems. Calc Var Partial Differ Equ. 2003;17:257–281.
- Bartolo P, Benci V, Fortunato D. Abstract critical theorems and applications to some nonlinear problems with strong resonance at infinity. Nonlinear Anal. 1983;7:981–1012.
- Schechter M. Linking methods in critical point theory. Boston: Birkhäuser; 1999.