RN上一类带有凹凸项的p-Kirchhoff方程无穷多解的存在性
Infinitely Many Solutions for a Class ofp-Kirchhoff Equations with Concave-Convex Terms on R N
DOI:10.12677/AAM.2024.136285,PDF,下载: 72浏览: 127科研立项经费支持
作者:刘立华：盐城师范学院数学与统计学院，江苏 盐城
关键词:p-Kirchhoff方程；喷泉引理；对偶喷泉引理；无穷多解；p-Kirchhoff Equation；Fountain Theorem；Dual Fountain Theorem；Infinitely Many Solutions
摘要:本文中，我们研究如下一类p-Kirchhoff椭圆方程 解的存在性，其中 是非负的权函数。 利用喷泉引理和对偶喷泉引理，我们得到了上述问题存在无穷多解。
Abstract:In this paper, we prove the multiplicity of solutions for the following p-Kirchhoff elliptic equation where are weight functions which may be unbounded or decaying to zero at infinity. By the methods of Fountain Theorem and Dual Fountain Theorem, we prove that above problem admits infinitely many solutions.
文章引用：刘立华. R N上一类带有凹凸项的p-Kirchhoff方程无穷多解的存在性[J]. 应用数学进展, 2024, 13(6): 2984-2995. https://doi.org/10.12677/AAM.2024.136285

参考文献

[1] Kirchhoff, G. (1883) Mechanik, Teubner, Leipzig.
[2] Alves, C.O., Corrˆea, F.J.S.A. and Ma, T.F. (2005) Positive Solutions for a Quasilinear Elliptic Equation of Kirchhoff Type. Computers & Mathematics with Applications, 49, 85-93.
https://doi.org/10.1016/j.camwa.2005.01.008
[3] Julio, F., Correa, S.A. and Figueiredo, G.M. (2006) On an Elliptic Equation of p-Kirchhoff Type via Variational Methods. Bulletin of the Australian Mathematical Society, 74, 263-277.
https://doi.org/10.1017/s000497270003570x
[4] Corrˆea, F.J.S.A. and Figueiredo, G.M. (2009) On a p-Kirchhoff Equation via Krasnoselskii’s Genus. Applied Mathematics Letters, 22, 819-822.
https://doi.org/10.1016/j.aml.2008.06.042
[5] Chen, C., Kuo, Y. and Wu, T. (2011) The Nehari Manifold for a Kirchhoff Type Problem Involving Sign-Changing Weight Functions. Journal of Differential Equations, 250, 1876-1908.
https://doi.org/10.1016/j.jde.2010.11.017
[6] Li, Y., Li, F. and Shi, J. (2012) Existence of a Positive Solution to Kirchhoff Type Problems without Compactness Conditions. Journal of Differential Equations, 253, 2285-2294.
https://doi.org/10.1016/j.jde.2012.05.017
[7] Liu, D. (2010) On p-Kirchhoff Equation via Fountain Theorem and Dual Fountain Theorem. Nonlinear Analysis: Theory, Methods Applications, 72, 302-308.
https://doi.org/10.1016/j.na.2009.06.052
[8] Liu, D. and Zhao, P. (2012) Multiple Nontrivial Solutions to p-Kirchhoff Equation. Nonlinear Analysis: Theory, Methods & Applications, 75, 5032-5038.
https://doi.org/10.1016/j.na.2012.04.018
[9] Wu, X. (2011) Existence of Nontrivial Solutions and High Energy Solutions for Schro¨dinger- Kirchhoff-Type Equations in RN . Nonlinear Analysis: Real World Applications, 12, 1278-1287.
https://doi.org/10.1016/j.nonrwa.2010.09.023
[10] Wu, T. (2006) On Semilinear Elliptic Equations Involving Concave-Convex Nonlinearities and Sign-Changing Weight Function. Journal of Mathematical Analysis and Applications, 318, 253-270.
https://doi.org/10.1016/j.jmaa.2005.05.057
[11] Willem, M. (1996) Minimax Theorem. Birkha¨user Boston,.
[12] Zhao, L., Li, A. and Su, J. (2012) Existence and Multiplicity Results for Quasilinear Elliptic Exterior Problems with Nonlinear Boundary Conditions. Nonlinear Analysis: Theory, Methods Applications, 75, 2520-2533.
https://doi.org/10.1016/j.na.2011.10.046
[13] Lin, X. and Tang, X.H. (2013) Existence of Infinitely Many Solutions p-Laplacian Equations in RN . Nonlinear Analysis: Theory, Methods & Applications, 92, 72-81.
https://doi.org/10.1016/j.na.2013.06.011
[14] Zhao, J. and Zhao, P.H. (2007) Infinitely Many Weak Solutions for a p-Laplacian Equation with Nonlinear Boundary Conditions. Electronic Journal of Differential Equations, 2007, 1-14.
[15] Ambrosetti, A. and Rabinowitz, P.H. (1973) Dual Variational Methods in Critical Point Theory and Applications. Journal of Functional Analysis, 14, 349-381.
https://doi.org/10.1016/0022-1236(73)90051-7
[16] Chen, C., Chen, L. and Xiu, Z. (2013) Existence of Nontrivial Solutions for Singular Quasilinear Elliptic Equations RN . Computers Mathematics with Applications, 65, 1909-1919.
https://doi.org/10.1016/j.camwa.2013.04.017
[17] Lyberopoulos, A.N. (2011) Quasilinear Scalar Field Equations with Competing Potentials. Journal of Differential Equations, 251, 3625-3657.
https://doi.org/10.1016/j.jde.2011.08.011

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