一类Kirchhoff-Choquard方程基态解的存在性
Existence of Groundstates for a Class of Kirchhoff-Choquard Equations
摘要: 本文研究一类带有势函数对数非线性项的𝐾𝑖𝑟𝑐ℎℎ𝑜𝑓𝑓 − 𝐶ℎ𝑜𝑞𝑢𝑎𝑟𝑑方程基态解的存在性, 通过𝐸𝑘𝑒𝑙𝑎𝑛𝑑变分方法, 对数𝑆𝑜𝑏𝑜𝑙𝑒𝑣不等式, 𝐻𝑎𝑟𝑑𝑦−𝐿𝑖𝑡𝑡𝑙𝑒𝑤𝑜𝑜𝑑−𝑆𝑜𝑏𝑜𝑙𝑒𝑣 不等式以及对对数非线项的技巧性处理,得到𝛼 ∈ (0, 3), 𝛼 = 0以及带有非线性扰动项等三种情况下𝐾𝑖𝑟𝑐ℎℎ𝑜𝑓𝑓−𝐶ℎ𝑜𝑞𝑢𝑎𝑟𝑑方程存在基态解的结论。
Abstract: In this paper, we consider the existence of ground state solutions for a class of Kirchhoff-Choquard equations with logarithmic nonlinear terms of potential functions by Ekeland variational method logarithmic Sobolev inequality and Hardy-Littlewood-Sobolev inequality. It is concluded that the Kirchhoff-Choquard equation has ground state solutions in 𝛼 ∈ (0, 3), 𝛼 = 0 and with nonlinear perturbation term.
文章引用：张凯月, 罗贤兵. 一类Kirchhoff-Choquard方程基态解的存在性[J]. 运筹与模糊学, 2022, 12(2): 429-443. https://doi.org/10.12677/ORF.2022.122045

参考文献

[1] Zhou, J. and Wu, Y.S. (2021) Existence of Solutions for a Class of Kirchhoff-Type Equations with Indefinite Potential. Boundary Value Problems, 12, Article No. 74. [Google Scholar] [CrossRef] 
[2] Zhou, F. and Yang, M.B. (2021) Solutions for a Kirchhoff Type Problem with Critical Exponent in RN. Journal of Mathematical Analysis and Applications, 494, Article ID: 124638.
[3] Vicente, A. (2022) Well-Posedness and Stability for Kirchhoff Equation with Non-Porous A-coustic Boundary Conditions. Journal of Differential Equations, 313, 25-38. [Google Scholar] [CrossRef] 
[4] Zhou, L. and Zhu, C.X. (2022) Ground State Solution for a Class of Kirchhoff-Type Equation with General Convolution Nonlinearity. Zeitschrift für angewandte Mathematik und Physik, 73, Article No. 75. [Google Scholar] [CrossRef] 
[5] Gu, G.Z. and Yang, Z.P. (2022) On the Singularly Perturbation Fractional Kirchhoff Equations: Critical Case. Advances in Nonlinear Analysis, 11, 1097-1116. [Google Scholar] [CrossRef] 
[6] Li, G. and Tang, C. (2018) Existence of a Ground State Solution for Choquard Equation with the Upper Critical Exponent. Computers and Mathematics with Applications, 76, 2635-2647. [Google Scholar] [CrossRef] 
[7] Li, F., Gao, C. and Liang, Z. (2018) Existence and Concentration of Nontrivial Nonnegative Ground State Solutions to Kirchhoff-Type System with Hartree-Type Nonlinearity. Zeitschrift für angewandte Mathematik und Physik, 69, Article No. 148.
[8] Li, G., Li, Y., Tang, C. and Yin, L. (2019) Existence and Concentrate Behavior of Ground State Solutions for Critical Choquard Equations. Applied Mathematics Letters, 96, 101-107. [Google Scholar] [CrossRef] 
[9] Gao, F.S. and Yang, M.B. (2017) On Nonlocal Choquard Equations with Hardy-Littlewood-Sobolev Critical Exponents. Journal of Mathematical Analysis and Applications, 448, 1006- 1041. [Google Scholar] [CrossRef] 
[10] Li, F.Y., Gao, C.J. and Zhu, X.L. (2017) Existence and Concentration of Sign-Changing Solutions to Kirchhoff-Type System with Hartree-Type Nonlinearity. Journal of Mathematical Analysis and Applications, 448, 60-80. [Google Scholar] [CrossRef] 
[11] Liu, H., Liu, Z. and Xiao, Q. (2017) Ground State Solution for a Fourth-Order Nonlinear Elliptic Problem with Logarithmic Nonlinearity. Applied Mathematics Letters, 79, 176-181. [Google Scholar] [CrossRef] 
[12] Schaftingen, J.V. and Xia, J. (2018) Groundstates for a Local Nonlinear Perturbation of the Choquard Equations with Lower Critical Exponent. Journal of Mathematical Analysis and Applications,464,1184-1202. [Google Scholar] [CrossRef] 
[13] Tian, S. (2017) Multiple Solutions for the Semilinear Elliptic Equations with the Sign-Changing Logarithmic Nonlinearity. Journal of Mathematical Analysis and Applications, 454, 816-828. [Google Scholar] [CrossRef] 
[14] Squassina, M. and Szulkin, A. (2015) Multiple Solutions to Logarithmic Schrödinger Equations with Periodic Potential. Calculus of Variations and Partial Differential Equations, 54, 585-597. [Google Scholar] [CrossRef] 
[15] Gao, F. and Yang, M. (2018) On the Brezis-Nirenberg Type Critical Problem for Nonlinear Choquard Equation. Science China Mathematics, 61, 1219-1242. [Google Scholar] [CrossRef] 
[16] Le, X.T. (2019) The Nehari Manifold for Fractional p-Laplacian Equation with Logarithmic Nonlinearity on Whole Space. Computers and Mathematics with Applications, 78, 3931-3940. [Google Scholar] [CrossRef] 
[17] Alves, C.O. and de Morais Filho, D.C. (2018) Existence and Concentration of Positive Solutions for a Schrödinger Logarithmic Equation. Zeitschrift für angewandte Mathematik und Physik, 69, Article No. 144. [Google Scholar] [CrossRef] 
[18] Chen, H. and Tian, S. (2015) Initial Boundary Value Problem for a Class of Semilinear Pseudo-Parabolic Equations with Logarithmic Nonlinearity. Journal of Differential Equations, 258, 4424-4442. [Google Scholar] [CrossRef] 
[19] Ji, C. and Szulkin, A. (2016) A Logarithmic Schrödinger Equation with Asymptotic Conditions on the Potential. Journal of Mathematical Analysis and Applications, 437, 241-254. [Google Scholar] [CrossRef] 
[20] Wang, J., Tian, L.X., Xu, J.X., et al. (2013) Erratum to: Existence and Concentration of Positive Solutions for Semilinear Schrödinger-Poisson Systems in R3. Calculus of Variations and Partial Differential Equations, 48, 275-276. [Google Scholar] [CrossRef] 
[21] Li, Y.H., Li, F.Y. and Shi, J.P. (2017) Existence and Multiplicity of Positive Solutions to Schrödinger-Poisson Type Systems with Critical Nonlocal Term. Calculus of Variations and Partial Differential Equations, 56, Article No. 134. [Google Scholar] [CrossRef] 
[22] Wang, Z.P. and Zhou, H.-S. (2015) Sign-Changing Solutions for Nonlinear Schrödinger-Poisson System in R3. Calculus of Variations and Partial Differential Equations, 52, 927-943. [Google Scholar] [CrossRef] 

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