本文研究了一类具有对数非线性的Kirchhoff-Choquard方程解的存在性。利用经典山路引理,证明了相应的能量泛函具有山路结构,且满足PS条件,从而方程至少存在一个非平凡解。In this article, the existence of solutions to a Kirchhoff-C...本文研究了一类具有对数非线性的Kirchhoff-Choquard方程解的存在性。利用经典山路引理,证明了相应的能量泛函具有山路结构,且满足PS条件,从而方程至少存在一个非平凡解。In this article, the existence of solutions to a Kirchhoff-Choquard equation with logarithmic nonlinearities is studied. By using the classical mountain pass lemma, we proved that the energy functional of the problem has a mountain pass structure and satisfies the PS condition, so the studies problem admits at least a nontrivial solution.展开更多
运用变分方法讨论一类Schrödinger-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 p...运用变分方法讨论一类Schrödinger-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 Schrödinger-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.展开更多
基金Supported by Tianyuan Fund for Mathematics of National Natural Science Foundation of China(A0324615)and Science Founda-tion of Nanjing Normal University(2002SXXXGQ2B20).
文摘本文研究了一类具有对数非线性的Kirchhoff-Choquard方程解的存在性。利用经典山路引理,证明了相应的能量泛函具有山路结构,且满足PS条件,从而方程至少存在一个非平凡解。In this article, the existence of solutions to a Kirchhoff-Choquard equation with logarithmic nonlinearities is studied. By using the classical mountain pass lemma, we proved that the energy functional of the problem has a mountain pass structure and satisfies the PS condition, so the studies problem admits at least a nontrivial solution.
文摘运用变分方法讨论一类Schrödinger-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 Schrödinger-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.
