带有变号权函数的p(x)-Kirchhoff类型方程正解的存在性与多重性
Multiplicity of Positive Solutions of p(x)-Kirchhoff Problems with Sign-Changing Weight Functions
DOI: 10.12677/AAM.2020.94068, PDF,   
作者: 尚 彬：浙江师范大学数学与计算机科学学院，浙江 金华
关键词: 正解；Nehari流形；变分法；p(x)-Kirchhoff方程；Positive Solution； Nehari Manifold； Variational Method； p(x)-Kirchhoff Equation
摘要: 本文研究带有变号权函数的p(x)-Kirchhoff类型方程，主要运用变分方法与Nehari流形的分解证明其正解的存在性与多重性。
Abstract: In this paper, the p(x)-Kirchhoff problem with sign-changing weight functions is studied. Based on variational method and Nehari manifold, it is proved the existence and multiplicity of positive so-lutions of the problem.
文章引用：尚彬. 带有变号权函数的p(x)-Kirchhoff类型方程正解的存在性与多重性[J]. 应用数学进展, 2020, 9(4): 565-573. https://doi.org/10.12677/AAM.2020.94068

参考文献

[1] Huang, J.C., Chen, C.S. and Xiu, Z.H. (2013) Existence and Multiplicity Results for a p-Kirchhoff Equation with a Concave-Convex Term. Applied Mathematics Letters, 26, 1070-1075. [Google Scholar] [CrossRef] 
[2] Chen, C.Y., Kuo, Y.C. and Wu, T.F. (2011) The Nehari Manifold for a Kirchhoff Type Problem Involving Sign- Changing Weight Functions. Journal of Differential Equations, 250, 1876-1908. [Google Scholar] [CrossRef] 
[3] Li, Y.X., Mei, M. and Zhang, K. (2016) Existence of Multiple Nontrivial Solutions for a p-Kirchhoff Type Elliptic Problem Involving Sign-Changing Weight Functions. Discrete and Continuous Dynamical Systems-Series B, 21, 883-908. [Google Scholar] [CrossRef] 
[4] Khaled, B.A. (2012) Multiplicity of Positive Solution of p(x)-Laplacian Problems with Sign-Changing Weight Functions. Advances in Pure and Applied Mathematics, 3, 202-221. [Google Scholar] [CrossRef] 
[5] Rasouli, S.H. and Fallah, K. (2017) The Nehari Manifold Approach for a p(x)-Laplacian Problem with Nonlinear Boundary Conditions. Ukrainian Mathematical Journal, 69, 111-125. [Google Scholar] [CrossRef] 
[6] Fan, X.L., Shen, J.S. and Zhao, D. (2001) Sobolev Embedding Theorems for Spaces . Journal of Mathematical Analysis and Applications, 262, 749-760. [Google Scholar] [CrossRef] 
[7] Zhang, X. and Liu, X. (2007) The Local Boundedness and Harnack Inequality of p(x)-Laplace Equation. Journal of Mathematical Analysis and Applications, 232, 209-218.

为你推荐