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在非齐次边界条件下一类非齐次Schrdinger-Poisson系统的多个解

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Keywords: Schrdinger-Poisson系统,Ekeland变分原理,山路引理

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Abstract:

研究了具有非齐次非线性扰动项和非齐次边界条件的一类Schrdinger-Poisson系统.Schrdinger-Poisson系统是非常重要的数学物理方程组,这类系统在物理上有很重要的意义,描述了带电粒子在电磁场运动,特别是在未给定势的电磁场里的相互作用.这类系统在其次边界条件下的各类情况均有人讨论,但在非齐次边界条件下具有非齐次非线性扰动项的此类系统没有讨论.于是从数学的角度可以看出此研究是必要的.主要用Ekeland变分原理和山路引理得到了此类Schrdinger-Poisson系统多个解的存在性结果.

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