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一类拟线性椭圆方程的规范基态解
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Abstract:
本文研究了拟线性椭圆方程
We study the quasilinear elliptic equation
[1] | Kurihara, S. (1981) Large-Amplitude Quasi-Solitons in Superfluid Films. Journal of the Physical Society of Japan, 50, 3262-3267. https://doi.org/10.1143/JPSJ.50.3262 |
[2] | Makhankov, V. and Fedyanin V. (1984) Non-Linear Effects in Quasi-One-Dimensional Models of Condensed Matter Theory. Physics Reports, 104, 1-86. https://doi.org/10.1016/0370-1573(84)90106-6 |
[3] | Quispel, G. and Capel, H. (1982) Equation of Motion for the Heisenberg Spin Chain. Physica A: Statistical Mechanics and its Applications, 110, 41-80. https://doi.org/10.1016/0378-4371(82)90104-2 |
[4] | Liu, J. and Wang, Z.-Q. (2003) Soliton Solutions for Quasilinear Schr?dinger Equations, I. Proceedings of the American Mathematical Society, 131, 441-448. https://doi.org/10.1090/S0002-9939-02-06783-7 |
[5] | Ruiz, D. and Siciliano, G. (2010) Existence of Ground States for a Modified Nonlinear Schr?dinger Equation. Nonlinearity, 23, 1221-1233. https://doi.org/10.1088/0951-7715/23/5/011 |
[6] | Colin, M. and Jeanjean, L. (2004) Solutions for a Quasilinear Schr?dinger Equation: A Dual Approach. Nonlinear Analysis, 56, 213-226. https://doi.org/10.1016/j.na.2003.09.008 |
[7] | Liu, J., Wang, Y. and Wang, Z.-Q. (2003) Soliton Solutions for Quasilinear Schr?dinger Equations, II. Journal of Differential Equations, 187, 473-493. https://doi.org/10.1016/S0022-0396(02)00064-5 |
[8] | Liu, J., Wang, Y. and Wang, Z.-Q. (2004) Solutions for Quasilinear Schr?dinger Equations via the Nehari Method. Communications in Partial Differential Equations, 29, 879-901. https://doi.org/10.1081/PDE-120037335 |
[9] | Liu, X., Liu, J. and Wang, Z.-Q. (2013) Quasilinear Elliptic Equations via Perturbation Method. Proceedings of the American Mathematical Society, 141, 253-263. https://doi.org/10.1090/S0002-9939-2012-11293-6 |
[10] | Jing, Y and Liu, H. (2022) Sign-Changing Solutions for a Modified Nonlinear Schr?dinger Equation in . Calculus of Variations and Partial Differential Equations, 61, 144. https://doi.org/10.1007/s00526-022-02266-9 |
[11] | Colin, M., Jeanjean, L. and Squassina, M. (2010) Stability and Instability Results for Standing Waves of Quasi-Linear Schr?dinger Equations. Nonlinearity, 23, 1353-1385. https://doi.org/10.1088/0951-7715/23/6/006 |
[12] | Zhang, L., Li, Y. and Wang, Z.-Q. (2023) Multiple Normalized Solutions for a Quasi-Linear Schr?dinger Equation via Dual Approach. Topological Methods in Nonlinear Analysis, 61, 465-489. https://doi.org/10.12775/TMNA.2022.052 |
[13] | Ye, H. and Yu, Y. (2021) The Existence of Normalized Solutions for L2-Critical Quasilinear Schr?dinger equations. Journal of Mathematical Analysis and Applications, 497, Article ID: 124839. https://doi.org/10.1016/j.jmaa.2020.124839 |
[14] | Jeanjean, L. and Luo, T. (2013) Sharp Nonexistence Results of Prescribed L2-Norm Solutions for Some Class of Schr?dinger-Poisson and Quasi-Linear Equations. Zeitschrift für angewandte Mathematik und Physik, 64, 937-954. https://doi.org/10.1007/s00033-012-0272-2 |
[15] | Jeanjean, L. and Luo, T. and Wang, Z.-Q. (2015) Multiple Normalized Solutions for Quasi-Linear Schr?dinger Equations. Journal of Differential Equations, 259, 3894-3928. https://doi.org/10.1016/j.jde.2015.05.008 |
[16] | Li, H. and Zou, W. (2023) Quasilinear Schr?dinger Equations: Ground State and Infinitely Many Normalized Solutions. Pacific Journal of Mathematics, 322, 99-138. https://doi.org/10.2140/pjm.2023.322.99 |
[17] | Zhang, L., Chen, J. and Wang, Z-Q. (2023) Ground States for a Quasilinear Schr?dinger Equation: Mass Critical and Supercritical Cases. Applied Mathematics Letters, 145, Article ID: 108763. https://doi.org/10.1016/j.aml.2023.108763 |
[18] | Agueh, M. (2008) Sharp Gagliardo-Nirenberg Inequalities via p-Laplacian Type Equations. Nonlinear Differential Equations and Applications NoDEA, 15, 457-472. https://doi.org/10.1007/s00030-008-7021-4 |