LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM
LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM
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发表时间：
2017
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通讯作者：
Ji Chao;Fei Fang;Binlin Zhang;Vicentiu D. Rădulescu
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作者：
Ji Chao;Fei Fang;Binlin Zhang;Vicentiu D. Rădulescu
本文讨论了Schr dinger-Poisson方程组− <$u+ V（x）u+ λφ（x）u = f（u），in R，− <$φ = u，in R的最小能量变号解的存在性.由于系统中引入了所谓的非局部项λφ（x）u，使得上述系统的变分泛函具有与λ = 0时完全不同的性质.利用约束变分方法和定量变形引理，证明了上述问题存在一个最小能量变号解。此外，对于任意λ > 0，我们证明了变号解的能量严格大于基态能量的两倍。最后，我们把λ作为参数，研究了当λ ≠ 0时最小能量变号解的收敛性.
This article concerns the existence of the least energy sign-changing solutions for the Schrödinger-Poisson system −∆u+ V (x)u+ λφ(x)u = f(u), in R, −∆φ = u, in R. Because the so-called nonlocal term λφ(x)u is involved in the system, the variational functional of the above system has totally different properties from the case of λ = 0. By constraint variational method and quantitative deformation lemma, we prove that the above problem has one least energy sign-changing solution. Moreover, for any λ > 0, we show that the energy of a sign-changing solution is strictly larger than twice of the ground state energy. Finally, we consider λ as a parameter and study the convergence property of the least energy sign-changing solutions as λ↘ 0.