Xianyong YANG
,
Wei ZHANG
,
Fukun ZHAO
. A NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC EQUATION VIA DUAL APPROACH[J]. Acta mathematica scientia, Series B, 2019
, 39(2)
: 580
-596
.
DOI: 10.1007/s10473-019-0220-8
[1] Brüll L, Lange H. Solitary waves for quasilinear Schrödinger equations. Exposition Math, 1986, 4(3):279-288
[2] Canino A, Degiovanni M. Nonsmooth critical point theory and quasilinear elliptic equations//Topological Methods in Differential Equations and Inclusions. Netherlands:Springer, 1995:1-50
[3] Chen J H, Tang X H, Cheng B T. Existence and nonexistence of positive solutions for a class of generalized quasilinear Schrödinger equations involving Kirchhoff-type perturbation with critical Sobolev exponent. J Math Phys, 2018, 59(2):021505, 24
[4] Chen S T, Tang X H. Ground state solutions for generalized quasilinear Schrödinger equations with variable potentials and Berestycki-Lions nonlinearities. J Math Phys, 2018, 59(8):081508, 18
[5] Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equation:a dual approach. Nonlinear Anal, 2004, 56(2):213-226
[6] Deng Y B, Guo Y X, Liu J Q. Existence of solutions for quasilinear elliptic equations with Hardy potential. J Math Phys, 2016, 57(3):031503, 15
[7] Deng Y B, Peng S J, Yan S S. Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations. J Differential Equations, 2016, 260(2):1228-1262
[8] do Ó J M B, Miyagaki O H, Soares S H M. Soliton solutions for quasilinear Schrödinger equations with critical growth. J Differential Equations, 2010, 248(4):722-744
[9] Deng Z Y, Huang Y S. On positive G-symmetric solutions of a weighted quasilinear elliptic equation with critical Hardy-Sobolev exponent. Acta Math Sci, 2014, 34B(5):1619-1633
[10] Gasiński L, Papageorgiou N S. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems. Boca Raton, FL:Chapman & Hall/CRC, 2005
[11] Jabri Y. The Mountain Pass Theorem. Cambridge:Cambridge University Press, 2003
[12] Li Q Q, Wu X. Existence of nontrivial solutions for generalized quasilinear Schrödinger equations with critical or supercritical growths. Acta Math Sci, 2017, 37B(6):1870-1880
[13] Li Z X, Shen Y T. Nonsmooth critical point theorems and its applications to quasilinear Schrödinger equations. Acta Math Sci, 2016, 36B(1):73-86
[14] Kurihara S. Exact soliton solution for superfluid film dynamics. J Phys Soc Japan, 1981, 50(11):3801-3805
[15] Liu J Q, Liu X Q, Wang Z Q. Multiple sign-changing solutions for quasilinear elliptic equations via perturbation method. Comm Partial Differential Equations, 2014, 39(12):2216-2239
[16] Liu J Q, Wang Y Q, Wang Z Q. Soliton solutions for quasilinear Schrödinger equations Ⅱ. J Differential Equations, 2003, 187(2):473-493
[17] Liu J Q, Wang Y Q, Wang Z Q. Solutions for quasilinear Schrödinger equations via the Nehari method. Comm Partial Differential Equations, 2004, 29(5/6):879-901
[18] Liu J Q, Wang Y Q, Wang Z Q. Soliton solutions for quasilinear Schrödinger equations I. Proc Amer Math Soc, 2003, 131(2):441-448
[19] Liu J Q, Wang Z Q, Guo Y X. Multibump solutions for quasilinear elliptic equations. J Funct Anal, 2012, 262(9):4040-4102
[20] Liu J Q, Wang Z Q, Wu X. Multibump solutions for quasilinear elliptic equations with critical growth. J Math Phys, 2013, 54(12):121501, 31
[21] Liu X Q, Liu J Q, Wang Z Q. Quasilinear elliptic equations via perturbation method. Proc Amer Math Soc, 2013. 141(1):253-263
[22] Lu W D. Variational Methods in Differential Equations. Scientific Publishing House in China, 2002
[23] Shen Y T, Wang Y J. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Anal., 2013, 80:194-201
[24] Shi H X, Chen H B. Existence and multiplicity of solutions for a class of generalized quasilinear Schrödinger equations. J Math Anal Appl, 2017, 452(1):578-594
[25] Wang Y J, Zou W M. Bound states to critical quasilinear Schrödinger equations. Nonlinear Differ Equ Appl, 2012, 19(1):19-47
[26] Willem M. Minimax theorems//Progress in Nonlinear Differential Equations and their Applications Vol 24, Boston, MA:Birkhäuser Boston, Inc, 1996
[27] Wu K. Positive solutions of quasilinear Schrödinger equations with critical growth. Appl Math Lett, 2015, 45:52-57
[28] Wu K, Wu X. Multiplicity of solutions for a quasilinear elliptic equation. Acta Math Sci, 2016, 36B(2):549-559
[29] Wu X, Wu K. Existence of positive solutions, negative solutions and high energy solutions for quasi-linear elliptic equations on RN. Nonlinear Anal:Real World Appl, 2014, 16:48-64
[30] Wu X, Wu K. Geometrically distinct solutions for quasilinear elliptic equations. Nonlinearity, 2014, 27(5):987-1001
[31] Yang R R, Zhang W, Liu X Q. Sign-changing solutions for p-biharmonic equations with Hardy potential in RN. Acta Math Sci, 2017, 37B(3):593-606
[32] Zhang J, Tang X H, Zhang W. Infinitely many solutions of quasilinear Schrödinger equation with signchanging potential. J Math Anal Appl, 2014, 420(2):1762-1775
