一类带变号权Kirchhoff方程解的存在性
Existence of Solution for Kirchhoff Equation with Sign-Changing Weight
DOI: 10.12677/AAM.2023.124161, PDF, HTML,  被引量   
作者: 陈莉萍：兰州理工大学理学院，甘肃 兰州
关键词: Kirchhoff方程；非局部项；变分法；变号权；Kirchhoff Equation； Nonlocal Term； Variation Methods； Sign-Changing Weight
摘要: 本文研究一类具有变号权的Kirchhoff方程, 解的存在性, 其中 a, b > 0, 3 < p < 5, V (x) 是一个连续的变号权且 lim|x|→∞ V (x) = V∞ < 0.
Abstract: In this paper, we deal with the existence result of Kirchhoff equation with sign- changing weight , where a, b > 0, 3 < p < 5, V (x) is a continuous and sign-changing function such that lim|x|→∞ V (x) = V∞ < 0.
文章引用：陈莉萍. 一类带变号权Kirchhoff方程解的存在性[J]. 应用数学进展, 2023, 12(4): 1567-1573. https://doi.org/10.12677/AAM.2023.124161

参考文献

[1] Kirchhoff, G. (1883) Mechanik. Teubner, Leipzig.
[2] Oplinger, D.W. (1960) Frequency Response of a Nonlinear Stretched String. The Journal of the Acoustical Society of America, 32, 1529-1538. [Google Scholar] [CrossRef] 
[3] Lions, J.L. (1978) On Some Questions in Boundary Value Problems of Mathematical Physics. In: North-Holland Mathematics Studies, Vol. 30, North-Holland, Amsterdam, New York, 284- 346. [Google Scholar] [CrossRef] 
[4] Alves, C.O. and Figueiredo, G.M. (2016) Multi-Bump Solutions for a Kirchhoff-Type Problem. dvances in Nonlinear Analysis, 5, 1-26. [Google Scholar] [CrossRef] 
[5] Deng, Y.B., Peng, S.J. and Shuai, W. (2015) Existence and Asymptotic Behavior of Nodal Solutions for the Kirchhoff-Type Problems in R3. Journal of Functional Analysis, 269, 3500- 3527. [Google Scholar] [CrossRef] 
[6] Deng, Y.B. and Shuai, W. (2018) Sign-Changing Multi-Bump Solutions for Kirchhoff-Type Equations in R3. Discrete and Continuous Dynamical Systems, 38, 3139-3168. [Google Scholar] [CrossRef] 
[7] Figueiredo, G.M., Ikoma, N. and Santos Jr., J.R. (2014) Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities. Archive for Rational Mechanics and Analysis, 213, 931-979. [Google Scholar] [CrossRef] 
[8] Guo, Z. (2015) Ground State for Kirchhoff Equations without Compact Condition. Journal of Differential Equations, 259, 2884-2902. [Google Scholar] [CrossRef] 
[9] He, X.M. and Zou, W.M. (2012) Existence and Concentration Behavior of Positive Solutions for a Kirchhoff Equation in R3. Journal of Differential Equations, 252, 1813-1834. [Google Scholar] [CrossRef] 
[10] He, Y., Li, G.B. and Peng, S.J. (2014) Concentrating Bound States for Kirchhoff Type Prob- lems in R3 Involving Critical Sobolev Exponents. Advanced Nonlinear Studies, 14, 483-510. [Google Scholar] [CrossRef] 
[11] He, Y. and Li, G.B. (2015) Standing Waves for a Class of Kirchhoff Type Problems in R3 In- volving Critical Sobolev Exponents. Calculus of Variations and Partial Differential Equations, 54, 3067-3106. [Google Scholar] [CrossRef] 
[12] He, Y. (2016) Concentrating Bounded States for a Class of Singularly Perturbed Kirchhoff Type Equations with a General Nonlinearity. Journal of Differential Equations, 261, 6178- 6220. [Google Scholar] [CrossRef] 
[13] Li, G.B. and Ye, H.Y. (2014) Existence of Positive Ground State Solutions for the Nonlinear Kirchhoff Type Equations in R3. Journal of Differential Equations, 257, 566-600. [Google Scholar] [CrossRef] 
[14] Li, Y.H., Li, F.Y. and Shi, J.P. (2012) Existence of a Positive Solution to Kirchhoff Type Problems without Compactness Conditions. Journal of Differential Equations, 253, 2285-2294. [Google Scholar] [CrossRef] 
[15] Mao, A. and Chang, H. (2016) Kirchhoff Type Problems in RN with Radial Potentials and Locally Lipschitz Functional. Applied Mathematics Letters, 62, 49-54. [Google Scholar] [CrossRef] 
[16] Naimen, D. (2014) The Critical Problem of Kirchhoff Type Elliptic Equations in Dimension Four. Journal of Differential Equations, 257, 1168-1193. [Google Scholar] [CrossRef] 
[17] Sun, J.T. and Wu, T.F. (2014) Ground State Solutions for an Indefinite Kirchhoff Type Prob- lem with Steep Potential Well. Journal of Differential Equations, 256, 1771-1792. [Google Scholar] [CrossRef] 
[18] Tang, X.H. and Cheng, B. (2016) Ground State Sign-Changing Solutions for Kirchhoff Type Problems in Bounded Domains. Journal of Differential Equations, 261, 2384-2402. [Google Scholar] [CrossRef] 
[19] Wang, D.B. (2020) Least Energy Sign-Changing Solutions of Kirchhoff-Type Equation with Critical Growth. Journal of Mathematical Physics, 61, Article ID: 011501. [Google Scholar] [CrossRef] 
[20] Wang, J., Tian, L.X., Xu, J.X. and Zhang, F.B. (2012) Multiplicity and Concentration of Positive Solutions for a Kirchhoff Type Problem with Critical Growth. Journal of Differential Equations, 253, 2314-2351. [Google Scholar] [CrossRef] 
[21] Xie, Q.L., Ma, S.W. and Zhang, X. (2016) Bound State Solutions of Kirchhoff Type Problems with Critical Exponent. Journal of Differential Equations, 261, 890-924. [Google Scholar] [CrossRef] 
[22] Yu, X. (2010) Existence Results for a Schro¨dinger-Poisson Equation. Mathematica Applicata, 23, 648-652.
[23] Willem, M. (1996) Minimax Theorems. Birkha¨user, Boston.

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