一类 p-Laplace 方程基态解的存在性与集中性
Existence and Concentration ofGround States for a Class ofp-Laplace Equation
DOI: 10.12677/PM.2023.132016, PDF, HTML,    国家自然科学基金支持
作者: 石影：浙江师范大学数学与计算机科学学院，浙江 金华
关键词: p-Laplace；基态解；存在性；集中性；p-Laplace； Ground States； Existence； Concentration
摘要: 本文研究 p-Laplace 方程:其中:。当n→∞时，有界函数Qn(x)的自焦核supp{Qn+}收缩为有限点集。我们采用约束极小和集中紧性原理证明 p-Laplace 方程基态解的存在性和集中性。
Abstract: In this paper, we study the following p-Laplace equation: where .Qn are bounded functions with self-focusing core supp Qn+ which shrinks to a finite set of points as n→∞. Via the constraint minimizing method and the concentration compactness principle, we prove the existence and concentration for ground states.
文章引用：石影. 一类 p-Laplace 方程基态解的存在性与集中性[J]. 理论数学, 2023, 13(2): 131-148. https://doi.org/10.12677/PM.2023.132016

参考文献

[1] Bonanno, G. and Livrea, R. (2003) Multiplicity Theorems for the Dirichlet Problem Involving the p-Laplacian. Nonlinear Analysis: Theory, Methods and Applications , 54, 1-7.[CrossRef] 
[2] Ferrero, A. and Gazzola, F. (2003) On Subcriticality Assumptions for the Existence of Ground States of Quasilinear Elliptic Equations. Advances in Differential Equations, 8, 1081-1106.[CrossRef] 
[3] Liu, S. (2010) On Ground States of Superlinear p-Laplacian Equations in RN. Journal of Mathematical Analysis and Applications, 361, 48-58. [Google Scholar] [CrossRef] 
[4] Costa, D.G. and Magalh~aes, C.A. (1995) Existence Results for Perturbations of the p- Laplacian. Nonlinear Analysis: Theory, Methods and Applications, 24, 409-418.[CrossRef] 
[5] Buryak, A.V., Trapani, P.D., Skryabin, D.V. and Trillo, S. (2002) Optical Solitons Due to Quadratic Nonlinearities: From Basic Physics to Futuristic Applications. Physics Reports, 370, 63-235.[CrossRef] 
[6] Afrouzi, G.A., Mahdavi, S. and Naghizadeh, Z. (2007) The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition. Nonlinear Analysis: Modelling and Control, 12, 143-155.
[7] Binding, P.A., Drabek, P. and Huang, Y. (1997) On Neumann Boundary Value Problems for Some Quasilinear Elliptic Equations. Electronic Journal of Differential Equations, 1997, 1-11.
[8] Wu, T. (2007) Multiplicity of Positive Solution of p-Laplacian Problems with Sign-Changing Weight Function. International Journal of Mathematical Analysis, 1, 557-563.
[9] Zhong, X. and Zou, W. (2014) A Concentration Behavior for Semilinear Elliptic Systems with Indefinite Weight. Acta Mathematica Sinica, English Series, 30, 2014-2026.[CrossRef] 
[10] Ackermann, N. and Szulkin, A. (2013) A Concentration Phenomenon for Semilinear Elliptic Equations. Archive for Rational Mechanics and Analysis, 207, 1075-1089.[CrossRef] 
[11] Fang, X. and Wang, Z. (2020) Limiting Profile of Solutions for Schrodinger Equations with Shrinking Self-Focusing Core. Calculus of Variations and Partial Differential Equations, 59, Article No. 129.[CrossRef] 

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