一类拟线性椭圆方程边值问题多解的存在性
Existence of Multiple Solutions for Boundary Value Problems of a Class of Quasilinear Elliptic Equations
DOI: 10.12677/AAM.2021.1010362, PDF,    科研立项经费支持
作者: 田意梅*, 陈 林#：伊犁师范大学数学与统计学院，新疆 伊宁
关键词: Nehari流形；纤维映射；椭圆方程；Nehari Manifold； Fiber Mapping； Elliptic Equations
摘要: 拟线性椭圆方程问题是数学学科中重要的研究内容之一。椭圆型微分方程解的存在性问题近年来得到人们的广泛关注，基于文献研究，本文研究一类拟线性椭圆方程边值问题多解的存在性，并验证了一系列引理和定理，运用Nehari流形和纤维映射方法证明了该问题至少有两个正解。
Abstract: The problem of quasilinear elliptic equation is one of the important research contents in mathematics. The existence of solutions for elliptic differential equations has attracted extensive attention in recent years. Based on literature research, this paper studies the existence of multiple solutions for a class of quasilinear elliptic equation boundary value problems, verifies a series of lemmas and theorems, and proves that the problem has at least two positive solutions by using Nehari manifold and fiber mapping method.
文章引用：田意梅, 陈林. 一类拟线性椭圆方程边值问题多解的存在性[J]. 应用数学进展, 2021, 10(10): 3436-3445. https://doi.org/10.12677/AAM.2021.1010362

参考文献

[1] Chen, C.S., Wang, Z.Q. and Wang, F.P. (2010) Existence and Nonexistence of Positive Solutions for Singular-Lapla- cian Equation. Boundary Value Problems, 2010, Article No. 607453. [Google Scholar] [CrossRef] 
[2] Xiu, Z.H. and Chen, C.S. (2013) Existence and Nonexistence of Solutions for a Singular Elliptic Problem with a Nonlinear Boundary Condition. Annales Polonici Mathematici, 109, 93-107. [Google Scholar] [CrossRef] 
[3] Brown, K.J. and Zhang, Y.P. (2003) The Nehari Manifold for a Semilinear Elliptic Equation with a Sign-Changing Weight Function. Journal of Differential Equations, 193, 481-499. [Google Scholar] [CrossRef] 
[4] Chen, C.S., Xiu, Z.H. and Huang, J.C. (2012) The Nehari Manifold and the Existence of Multiple Solutions for a Singular Quasilinear Elliptic Equation. Journal of Mathematical Analysis and Applications, 393, 671-679. [Google Scholar] [CrossRef] 
[5] Brown, K.J. and Wu, T.F. (2007) A Fibering Map Approach to a Semilinear Elliptic Boundary Value Problem. Electronic Journal of Differential Equations, 2007, 1-9.
[6] Chen, C.S., Liu, L.H. and Chen, L. (2013) Multiple Solutions for Nonhomogeneous p-Laplacian Equations with Nonlinear Boundary Conditions on . Journal of Mathematical Analysis and Applications, 408, 432-441. [Google Scholar] [CrossRef] 

为你推荐