一类带有对数非线性项的拟线性椭圆方程解的存在性及多重性
Existence and Multiplicity of Solutions for a Class of Quasilinear Elliptic Equations with Logarithmic Nonlinearity
DOI: 10.12677/PM.2022.123044, PDF,   
作者: 刘晓莉：上海理工大学，上海
关键词: 拟线性；弱下半连续；非光滑；Quasilinear； Weak Lower Semicontinuous； Nonsmooth
摘要: 本文讨论一类带有对数非线性项的拟线性椭圆方程解的存在性和多重性。对主项系数A(x,t)提出合适的条件，使用弱下半连续泛函的非光滑临界点定理证明该问题存在山路解和无穷多非平凡解。
Abstract: In this paper, we consider the existence and multiplicity of solutions of a class of quasilinear elliptic equations with logarithmic nonlinearity. Under some appropriate conditions for the principal coefficient A(x,t), we use the nonsmooth critical point theorem of weak lower semicontinuous functional to prove the problem has mountain path solutions and infinite nontrivial solutions.
文章引用：刘晓莉. 一类带有对数非线性项的拟线性椭圆方程解的存在性及多重性[J]. 理论数学, 2022, 12(3): 400-410. https://doi.org/10.12677/PM.2022.123044

参考文献

[1] Candela, A.M. and Palmieri, P.G. (2009) Infinitely Many Solutions of Some Nonlinear Variational Equations. Calculus of Variations and Partial Differential Equations, 34, 495-530. [Google Scholar] [CrossRef] 
[2] Candela, A.M., Palmieri, G. and Salvatore, A. (2020) Multiple Solutions for Some Symmetric Supercritical Problems. Communications in Contemporary Mathematics, 22, Article ID: 1950075. [Google Scholar] [CrossRef] 
[3] Candela, A.M. and Salvatore, A. (2020) Existence of Radial Bounded Solutions for Some Quasilinear Elliptic Equations in RN. Nonlinear Analysis, 191, Article ID: 111625. [Google Scholar] [CrossRef] 
[4] Squassina, M. and Szulkin, A. (2015) Multiple Solutions to Loga-rithmic Schrödinger Equations with Periodic Potential. Calculus of Variations and Partial Differential Equations, 54, 585-597. [Google Scholar] [CrossRef] 
[5] Ji, C. and Szulkin, A. (2016) A Logarithmic Schrö-dinger Equation with Asymptotic Conditions on the Potential. Journal of Mathematical Analysis and Applications, 437, 241-254. [Google Scholar] [CrossRef] 
[6] Alves, C.O. and de Morais Filho, D.C. (2018) Existence and Concentration of Positive Solutions for a Schrödinger Logarithmic Equation. Zeitschrift Angewandte Mathematik und Physik, 69, 144. [Google Scholar] [CrossRef] 
[7] Alves, C.O., de Morais Filho, D.C. and Figueiredo, G.M. (2019) On Concentration of Solution to a Schrödinger Logarithmic Equation with Deepening Potential Well. Mathematical Methods in the Applied Sciences, 42, 4862-4875. [Google Scholar] [CrossRef] 
[8] Willem, M. (1996) Minimax Theorems. Birkhäuser, Boston. [Google Scholar] [CrossRef] 
[9] Avenia, P.D., Montefusco, D. and Squassina, M. (2014) On the Logarithmic Schrödinger Equation. Communications in Contemporary Mathematics, 16, Article ID: 1350032. [Google Scholar] [CrossRef] 
[10] Campa, I. and Degiovanni, M. (2000) Subdifferential Calculus and Nonsmooth Critical Point Theory. SIAM Journal on Optimization, 10, 1020-1048. [Google Scholar] [CrossRef] 
[11] Degiovanni, M. and Zani, S. (2000) Multiple Solutions of Semilinear Elliptic Equations with One-Sided Growth Conditions. Mathematical and Computer Modelling, 32, 1377-1393. [Google Scholar] [CrossRef] 
[12] Pellacci, B. and Squassina, M. (2004) Un-bounded Critical Points for a Class of Lower Semicontinuous Functionals. Journal of Differential Equations, 201, 25-62. [Google Scholar] [CrossRef] 

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