Abstract
In this paper, we consider the existence of solutions for critical quasilinear equations with singular potentials via perturbation method. We apply the generalization of Lions-type theorem to overcome the non-compactness problem.
Similar content being viewed by others
References
Colin, M., Jeanjean, L.: Solutions for a quasilinear Schrödinger equation: a dual approach. Nonlinear Anal. 56(2), 213–226 (2004)
do Ó, J., Miyagaki, O., Soares, S.: Soliton solutions for quasilinear Schrödinger equations with critical growth. J.Differential Equations 248, 722–744 (2010)
Guarnotta, U., Marano, S., Moussaoui, A.: Singular quasilinear convective elliptic systems in \(\mathbb{R} ^{N}\). Adv. Nonlinear Anal. 11(1), 741–756 (2022)
Jeanjean, L., Rădulescu, V.: Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases. J. Anal. Math. (2021). https://doi.org/10.1007/s11854-021-0170-7
Kurihura, S.: Large-amplitude quasi-solitons in superfluid films. J. Phys. Soc. Jpn. 50, 3262–3267 (1981)
Liu, J., Wang, Z.: Soliton solutions for quasilinear Schrödinger equations: I. Proc. Am. Math. Soc. 131(2), 441–448 (2003)
Liu, J., Wang, Y., Wang, Z.: Soliton solutions for quasilinear Schrödinger equations. II. J. Differential Equations 187(2), 473–493 (2003)
Liu, J., Wang, Y., Wang, Z.: Solutions for quasilinear Schrödinger equations via the Nehari method. Comm. Partial Differential Equations 29(5–6), 879–901 (2004)
Liu, X., Liu, J., Wang, Z.: Quasilinear elliptic equations with critical growth via perturbation method. J. Differential Equations 254(1), 102–124 (2013)
Liu, X., Liu, J., Wang, Z.: Quasilinear elliptic equations via perturbation method. Proc. Am. Math. Soc. 141(1), 253–263 (2013)
Poppenberg, M., Schmitt, K., Wang, Z.: On the existence of soliton solutions to quasilinear Schrödinger equations. Calc. Var. Partial Differential Equations 14(3), 329–344 (2002)
Qin, D., Rădulescu, V., Tang, X.: Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations. J. Differential Equations 275, 652–683 (2021)
Ruiz, D., Siciliano, G.: Existence of ground states for a modified nonlinear Schrödinger equation. Nonlinearity 23(5), 1221–1233 (2010)
Su, J., Wang, Z., Willem, M.: Nonlinear Schrödinger equations with unbounded and decaying potentials. Commun. Contemp. Math. 9, 571–583 (2007)
Su, Y.: Positive solution to Schrödinger equation with singular potential and double critical exponents, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31, 667–698 (2020)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Michael Kunzinger.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
H. Shi is supported by the Natural Science Foundation of Hunan Province (Grant No.2019JJ50096).
Rights and permissions
About this article
Cite this article
Su, Y., Shi, H. Critical quasilinear equations with singular potentials via perturbation method. Monatsh Math 199, 627–644 (2022). https://doi.org/10.1007/s00605-022-01747-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-022-01747-5