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临界或超临界增长分数阶Schrödinger—Poisson方程正解的存在性
王文波, 周见文, 李永昆, 李全清
数学学报 ›› 2021, Vol. 64 ›› Issue (2) : 269-280.
PDF(499 KB)
PDF(499 KB)
临界或超临界增长分数阶Schrödinger—Poisson方程正解的存在性
Existence of Positive Solutions for Fractional Schrödinger-Poisson System with Critical or Supercritical Growth
本文研究如下分数阶Schrödinger—Poisson方程
其中s ∈（4/3，1），t ∈（0，1），f是在原点超线性无穷远次临界的连续非线性项，指数q ≥ 2s*=（3-2s）/6.当λ>0充分小时，我们利用变分方法证明上述问题正解的存在性.本文的主要贡献是处理了超临界情形.
We study the following fractional Schrödinger-Poisson system
where s ∈ (4/3, 1), t ∈ (0, 1), the continuous function f is superlinear at zero and subcritical at infinity and the exponent q ≥ 2s*=(3-2s)/6. We obtain a positive solution of the above problem for small λ > 0 via the variational method. Our main contribution is that we can deal with the supercritical case.
分数阶Schrö / dinger&mdash / Poisson方程 / 临界或超临界增长 / Moser迭代 {{custom_keyword}} /
fractional Schrö / dinger-Poisson system / critical or supercritical growth / Moser iteration {{custom_keyword}} /
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国家自然科学基金资助项目（11901514，11861072，11961078，11561072，11801153）
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