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一类Schr?dinger-Kirchhoff-Poisson方程的正解
Positive Solutions for a Class of Schr?dinger-Kirchhoff-Poisson Equation

DOI: 10.12677/aam.2024.139415, PP. 4353-4359

Keywords: Schr?dinger-Kirchhoff-Poisson方程,正解,山路引理,变分法
Schr?dinger-Kirchhoff-Poisson Equation
, Positive Solutions, Mountain Pass Lemma, Variational Method

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Abstract:

运用变分方法讨论一类Schr?dinger-Kirchhoff-Poisson方程正解的存在性。在适当假设下,通过运用一些技巧证明了能量泛函满足Palais-Smale条件。最后运用山路引理,Ekeland变分原理和强极大值原理得到了主要结论。
The existence of positive solutions for a class of Schr?dinger-Kirchhoff-Poisson equation is discussed by using variational methods. Under appropriate assumption, it is proved that the energy functional satisfies the Palais-Smale condition by using some techniques. Finally, the main conclusions are obtained by using mountain pass lemma, Ekeland variational principle and strong maximum principle.

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