On a class of quasilinear equations with -1 powers*

doi:10.7523/j.ucas.2023.006

Abstract

CLC Number:

O175.29

Zhang Heng, Sun Yijing. On a class of quasilinear equations with -1 powers^*[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2023.006.

[1] Kurihara S.Large-amplitude quasi-solitons in superfluid films[J]. Journal of the Physical Society of Japan, 1981, 50(10):3262-3267.DOI:10.1143/jpsj.50.3262.
[2] Hartmann B, Zakrzewski W J.Electrons on hexagonal lattices and applications to nanotubes[J]. Physical Review B, 2003, 68(18):184302.DOI:10.1103/physrevb.68.184302.
[3] Kosevich A M, Ivanov B A, Kovalev A S.Magnetic solitons[J]. Physics Reports, 1990, 194(3/4):117-238.DOI:10.1016/0370-1573(90)90130-T.
[4] Makhankov V G, Fedyanin V K.Non-linear effects in quasi-one-dimensional models of condensed matter theory[J]. Physics Reports, 1984, 104(1):1-86.DOI:10.1016/0370-1573(84)90106-6.
[5] Liu J Q, Wang Y Q, Wang Z Q.Soliton solutions for quasilinear Schrödinger equations, II[J]. Journal of Differential Equations, 2003, 187(2):473-493.DOI:10.1016/s0022-0396(02)00064-5.
[6] Fang X D, Szulkin A.Multiple solutions for a quasilinear Schrödinger equation[J]. Physics Reports, 2013, 254(4):2015-2032.DOI:10.1016/j.jde.2012.11.017.
[7] Liu X Q, Liu J Q, Wang Z Q.Quasilinear elliptic equations via perturbation method[J]. Proceedings of the American Mathematical Society, 2013, 141(1):253-263.DOI:10.1090/s0002-9939-2012-11293-6.
[8] Agarwal R P, O’Regan D.Singular differential and integral equations with applications[M]. Springer Science & Business Media, 2003.DOI:10.1007/978-94-017-3004-4.
[9] Hernández J, Mancebo F J.Singular elliptic and parabolic equations[J]. In Handbook of differential equations:stationary partial differential equations, 2006, 3:317-400.DOI:10.1016/s1874-5733(06)80008-2.
[10] Marcos do Ó J, Moameni A.Solutions for singular quasilinear Schrödinger equations with one parameter[J]. Communications on Pure & Applied Analysis, 2010, 9(4):1011-1023.DOI:10.3934/cpaa.2010.9.1011.
[11] Santos C A, Yang M B, Zhou J Z.Global multiplicity of solutions for a modified elliptic problem with singular terms *[J]. Nonlinearity, 2021, 34(11):7842-7871.DOI:10.1088/1361-6544/ac2a50.
[12] Alves R L, Reis M.About existence and regularity of positive solutions for a quasilinear Schrödinger equation with singular nonlinearity[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2020, 60:1-23.DOI:10.14232/ejqtde.2020.1.60.
[13] Sun Y J.Compatibility phenomena in singular problems[J]. Proceedings of the Royal Society of Edinburgh Section A:Mathematics, 2013, 143(6):1321-1330.DOI:10.1017/s030821051100117x.
[14] Alves R L.Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2022, 13:1-29.DOI:10.14232/ejqtde.2022.1.13.
[15] Liu J Y, Liu D C, Zhao P H.Soliton solutions for a singular Schrödinger equation with any growth exponents[J]. Acta Applicandae Mathematicae, 2017, 148(1):179-199.DOI:10.1007/s10440-016-0084-z.
[16] do Ó J M B, Miyagaki O H, Soares S H M.Soliton solutions for quasilinear Schrödinger equations:the critical exponential case[J]. Nonlinear Analysis:Theory, Methods & Applications, 2007, 67(12):3357-3372.DOI:10.1016/j.na.2006.10.018.
[17] do Ó J M B, Miyagaki O H, Soares S H M.Soliton solutions for quasilinear Schrödinger equations with critical growth[J]. Journal of Differential Equations, 2010, 248(4):722-744.DOI:10.1016/j.jde.2009.11.030.
[18] Colin M, Jeanjean L.Solutions for a quasilinear Schrödinger equation:a dual approach[J]. Nonlinear Analysis:Theory, Methods & Applications, 2004, 56(2):213-226.DOI:10.1016/j.na.2003.09.008.
[19] Lazer A C, McKenna P J.On a singular nonlinear elliptic boundary-value problem[J]. Proceedings of the American Mathematical Society, 1991, 111(3):721.DOI:10.1090/s0002-9939-1991-1037213-9.

On a class of quasilinear equations with -1 powers^*

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 2

Recommended Articles

Metrics

Comments

[1]	CAO Xiaoqiang, SUN Yijing. Positive solutions to Kirchhoff-type problem with singular nonlinearity [J]. , 2014, 31(1): 5-9.
[2]	Zhao Pingfu, Qin Mengzhao. Multisymplectic Geometrical Approach for the Variational PDEs Connected with the Characteristics of the Vector Fields [J]. , 2003, 20(2): 160-167.