一类非线性椭圆型边界值问题的正解
Positive Solutions for a Class of Nonlinear Elliptic Boundary Value Problem
DOI: 10.12677/AAM.2018.77103, PDF,    国家自然科学基金支持
作者: 曲广军：陕西理工大学，数学与计算机科学学院，陕西 汉中
关键词: 欧拉变分原理；变形的山路引理；正解；Ekeland’s Variantional Principle； Variant Version Mountain Pass Lemma； Positive Solutions
摘要: 利用欧拉变分原理以及一个变形的山路引理，证明了一类非线性椭圆型边界值问题至少存在两个正解。
Abstract: Using the Ekeland’s variantional principle and a variant version mountain pass lemma, two positive solutions are obtained for a class of nonlinear elliptic boundary value problem.
文章引用：曲广军. 一类非线性椭圆型边界值问题的正解[J]. 应用数学进展, 2018, 7(7): 857-862. https://doi.org/10.12677/AAM.2018.77103

参考文献

[1] Zhou, H.S. (1998) Positive Solution for a Semilinear Elliptic Equations Which Is Almost Linear at Infinity. Zeitschrift für Angewandte Mathematik und Physik, 49, 896-906. [Google Scholar] [CrossRef] 
[2] Miyagaki, O.H. and Souto, M.A.S. (2008) Super-Linear Problems without Ambrosetti and Rabinowitz Growth Condition. Differential Equations, 245, 3628-3638. [Google Scholar] [CrossRef] 
[3] Willem, M. and Zou, W. (2003) On a Schrodinger Equation with Periodic Potential and Spectrum Point Zero. Indiana University Mathematics, 52, 109-132. [Google Scholar] [CrossRef] 
[4] Chen, Z.H., Shen, Y.T. and Yao, Y.X. (2003) Some Existence Results of Solutions for p-Laplacian. Acta Mathematica Scientia, 23B, 487-496. [Google Scholar] [CrossRef] 
[5] Li, G.B. and Zhou, H.S. (2001) Asymptotically Linear Dirichlet Problem for p-Laplacian. Nonlinear Analysis, 43, 1043-1055. [Google Scholar] [CrossRef] 
[6] 高婷梅. 含有一个参数的p-拉普拉斯方程正解的存在性[J]. 郑州大学学报(理学版), 2014, 46(3): 9-12.
[7] Schechter, M. (1991) A Variation of the Mountain Pass Lemma and Applications. Journal of the London Mathematical Society. Second Series, 44, 491-502. [Google Scholar] [CrossRef] 

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