一类p-Laplace方程基态解的存在性
Existence of Ground State Solutions for a Class of p-Laplace Equations
DOI: 10.12677/AAM.2023.121044, PDF, HTML, 下载: 220  浏览: 309  国家自然科学基金支持
作者: 刘文静, 许丽萍*：河南科技大学数学与统计学院，河南洛阳
关键词: p-Laplace方程；Pohozaev恒等式；变分法；基态解；p-Laplace Equations； Pohozaev Equality； Variational Methods； Ground State Solutions
摘要: 文章研究了如下形式的p-Laplace方程： 其中 , 常数V>0。当非线性项/在无穷远处满足超线性但不满足通常的 Ambrosetti-Rabinowitz (简称AR)条件时，通过运用新的技巧，借助Pohozaev恒等式, 获得了上述方程基态解的存在性，所得结果推广了相关文献的研究成果。
Abstract: In this paper, we study the following p-Laplace type equation: where and V > 0 is constant. By introducing some new tricks and Pohozaev equality, when the nonlinear function / satisfies the superlinear condition at infinity, the existence of ground state solution of this equation is obtained without assuming Ambrosetti - Rabinowitz type condition. Our results generalize the research results of related literatures.
文章引用：刘文静, 许丽萍. 一类p-Laplace方程基态解的存在性[J]. 应用数学进展, 2023, 12(1): 411-427. https://doi.org/10.12677/AAM.2023.121044

参考文献

[1] 杨玉蓓.一类双调和方程基态解的存在性丨4湖北大学学报：自然科学版，2014; 36(1): 35>40.
[2] Kusano, T. and Swanson* C.A. (1985) Entire Positive Solutions of Singular Semilinear Elliptic Equations. Japanese Journal of Mathematics. 111. 145-155.
https: //doi.org/10.4099/rnatb 1924.11.145
[3] Wu, S. and Yaug. H. (1997) The Existence TheoreiiLS for a Class of Subliuear Elliptic Exjuation in E,v. Actu Mathematica Sinica. 13. 259-304.
https://doi.org/10.1007/BF02560009
[4] 杨玉蓓，何毅.带有一般非线性项的一类p拉普拉斯型方程基态解的存在性问.科技通报，2017, 33(11): 24-26, 38.
[5] 邓义华，罗李平，周立君•一类带负位势函数的超线性P-Lapl■方程基态解的存在性[J]•数学物 理学报：A 辑，2015, 35(3): 578-586.
[6] Wang, W.Q. and MJK>, A.M. (2022) The Existence and Non-Existence of Sigu*Cliangiug Solu¬tions to Bi-Harmoiiic Equations with a p-Laplacian. Acta Mathematica Scientia, 42, 551-500.
https://doi.org/10.1007/sl0473-022-0209-6
[7] Wang, X., Qm, X.Q., Hu. G., tt ai (2018) Singular Elliptic Problems with Fractional Lapla- cian. Pure and Applied Mathematics, 34, 431-440.
[8] Bartsch. T. and Liu. Z.L. (2004) On a Superlinear Elliptic p-Laplacian Equation. Journal of Differential Equations. 198, 149-175.
https://doi.Org/10.1016/j.jde.2003.08.001
[9] Dogiovuiini. M. and Lancolotti, S. (2007) Linking over Cones arid Nontrivial Solutions for p-Laplace Equations with p-Superlinear Noiiliiioaxitv. Annates de Vlnstitut Henn Poincare Analyse Non Lineaii'e. 24, 007-919.
https://doi.Org/10.1016/j.anilipc.2006.06.007
[10] Alves, C.O. and Figueiredo, G.M. (2006) Existence and Multiplicity of Positive SolutioiLS to a p-Laplaciaii Equation in Differential and Int&jral Equations. 19, 143-162.
https: / / doi.org/10.57262/die/1356050522
[11] Chen, Y. and Tang. X.H. (2014) Ground State Solutions for p-Superliuear p-Laplacian Equa¬tions. Journal of the AvMmlian Mathematical Society. 97. 48-62.
https://doi.org/10.1017/S1446788714000135
[12] 赵艳.非线性椭圆方程或系统正基态解的存在性1硕士学位论文].南京：南京师范大学， 2012.
[13] Zou, W.M. and Schechter, M. (2006) Critical Point Theory and Its Applications. Springer, Berlin.
[14] D5Aprile, T. and Mugrial, D. (2004) Non-Existence Results for the Coupled Klein-Gordou- Maxwell Equations. Advanced Nonlinear Studies. 4. 307-322.
https: / /doi.org/10.1515/aus-2004- 0305
[15] Pucci； P. and Serrin. J. (1986) A General Variational Identity. Indiana University Mathematics Joumal 35, 681-703.
https://doi.org/10.1512/iumj.1986.35.35036
[16] Li, G.B. and Warig, C.H. (2011) The Existence of a Nontrivial Solution to a Nonlinear Elliptic Problem of Linking Type without the Ambrasetti-Rabiuowitz Condition. Annales Academicn Scientiamm Ftnnicai Matfiernatica, 36, 461-480.
https://doi.org/10.5186/aasfm.2011.3627
[17] Jeanjeau, L. (1997) Existence of Solutions with Prescribed Norm for Seinilinear Elliptic Equa¬tions. Nonlinear Anulyais. 28, 1633-1659.
https://doi.org/10.1016/S0362-〇46X(96)00021-1
[18] LioiLS, P.L. (1984) The Concentratioii-Compactiiess Principle in the Calculus of WriatioiLS. The Locally Compact Case, Part 1. Annales de Vhistitut Henri Poincare Analyse Non Lineaire. 1. 109-145.
https://doi.org/10.1016/s0294-1449(16)30428-0

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