一类拟线性薛定谔方程Robin边值问题变号解的存在性
Existence of Nodal Solutions for a Class of Quasilinear Schrödinger Equations with Robin Boundary Condition
DOI: 10.12677/pm.2025.1510259, PDF,    科研立项经费支持
作者: 邓 音：上海出版印刷高等专科学校，基础教学部，上海
关键词: 拟线性薛定谔方程；Robin边值；Nehari流形；变号解；Quasilinear Schrödinger Equation； Robin Boundary； Nehari Manifold； Nodal Solutions
摘要: 本文研究一类拟线性薛定谔方程Robin边值问题。通过Nehari流形方法和形变引理等，得到方程存在只变号一次的光滑变号解。
Abstract: We consider a quasilinear Schrödinger equation with Robin boundary condition. By using the Nehari manifold method and deformation lemma, we establish the existence of smooth nodal solutions that change sign exactly once.
文章引用：邓音. 一类拟线性薛定谔方程Robin边值问题变号解的存在性[J]. 理论数学, 2025, 15(10): 159-169. https://doi.org/10.12677/pm.2025.1510259

参考文献

[1] Porkolab, M. and Goldman, M.V. (1976) Upper-Hybrid Solitons and Oscillating-Two-Stream Instabilities. The Physics of Fluids, 19, 872-881. [Google Scholar] [CrossRef] 
[2] Laedke, E.W., Spatschek, K.H. and Stenflo, L. (1983) Evolution Theorem for a Class of Perturbed Envelope Soliton Solutions. Journal of Mathematical Physics, 24, 2764-2769. [Google Scholar] [CrossRef] 
[3] Kurihara, S. (1981) Large-Amplitude Quasi-Solitons in Superfluid Films. Journal of the Physical Society of Japan, 50, 3262-3267. [Google Scholar] [CrossRef] 
[4] Colin, M. and Jeanjean, L. (2004) Solutions for a Quasilinear Schrödinger Equation: A Dual Approach. Nonlinear Analysis: Theory, Methods & Applications, 56, 213-226. [Google Scholar] [CrossRef] 
[5] Moameni, A. and Offin, D.C. (2010) Positive Solutions for Singular Quasilinear Schrödinger Equations with One Parameter, II. Journal of Partial Differential Equations, 23, 222-234.
[6] Figueiredo, G.M., Santos Júnior, J.R. and Suárez, A. (2018) Structure of the Set of Positive Solutions of a Non-Linear Schrödinger Equation. Israel Journal of Mathematics, 227, 485-505. [Google Scholar] [CrossRef] 
[7] dos Santos, G., Figueiredo, G.M. and Severo, U.B. (2019) Multiple Solutions for a Class of Singular Quasilinear Problems. Journal of Mathematical Analysis and Applications, 480, Article 123405. [Google Scholar] [CrossRef] 
[8] Figueiredo, G.M., Ruviaro, R. and Junior, J.C.O. (2020) Quasilinear Equations Involving Critical Exponent and Concave Nonlinearity at the Origin. Milan Journal of Mathematics, 88, 295-314. [Google Scholar] [CrossRef] 
[9] Figueiredo, G.M., Severo, U.B. and Siciliano, G. (2020) Multiplicity of Positive Solutions for a Quasilinear Schrödinger Equation with an Almost Critical Nonlinearity. Advanced Nonlinear Studies, 20, 933-963. [Google Scholar] [CrossRef] 
[10] Liu, J., Wang, Y. and Wang, Z. (2004) Solutions for Quasilinear Schrödinger Equations via the Nehari Method. Communications in Partial Differential Equations, 29, 879-901. [Google Scholar] [CrossRef] 
[11] Deng, Y., Jia, G. and Li, F.L. (2020) Multiple Solutions to a Quasilinear Schrödinger Equation with Robin Boundary Condition. AIMS Mathematics, 5, 3825-3839. [Google Scholar] [CrossRef] 
[12] Deng, Y. and Jia, G. (2022) Multiple Solutions for a Quasilinear Schrödinger Equation Involving Critical Hardy-Sobolev Exponent with Robin Boundary Condition. Complex Variables and Elliptic Equations, 67, 2602-2618. [Google Scholar] [CrossRef] 
[13] 程永宽, 沈尧天. 含参数拟线性薛定谔方程的特征值问题[J]. 数学年刊A辑(中文版), 2023, 44(2): 113-120.
[14] Evans, L.C. (2010) Partial Differential Equations. 2nd Edition, American Mathematical Society.
[15] Willem, M. (1996) Minimax Theorems. Birkhäuser.
[16] Lieberman, G.M. (1988) Boundary Regularity for Solutions of Degenerate Elliptic Equations. Nonlinear Analysis: Theory, Methods & Applications, 12, 1203-1219. [Google Scholar] [CrossRef] 

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