一类非线性Schrödinger-Maxwell方程基态解的存在性OACSTPCD
EXISTENCE OF GROUND STATE SOLUTIONS FOR A CLASS OF NONLINEAR SCHR?DINGER-MAXWELL EQUATIONS
本文研究了如下Schr?dinger-Maxwell方程基态解的存在性问题({-△u+V (x)u+K(x)φ(x)u=b(x)|u|p-1u+λg(x, u) in R3,-△φ=K(x)u2in R3,)其中λ＞0, V (x)∈C1(R3, R), 且V (x)＞0. 在K, g, b 满足一定的假设条件下, 且0＜p＜1 时, 利用变分法和临界点理论,获得了基态解的存在性. 该结论推广了文献[7]的结果.
In this paper, we study the existence of ground state solutions for Schr?dinger-Maxwell equations({-△u+V (x)u+K(x)φ(x)u=b(x)|u|p-1u+λg(x, u) in R3,-△φ=K(x)u2in R3,) where λ＞0, V (x)∈C1(R3, R) and V (x)＞0. Under certain assumptions on K, g and 0＜p＜1, we obtain the ground state solutions by using variational methods and critical point theory, which promotes the results of literature [7] .
汪敏庆;黄文念;方立婉
广西师范大学数学与统计学院,广西桂林 541006广西师范大学数学与统计学院,广西桂林 541006广西师范大学数学与统计学院,广西桂林 541006
数理科学
Schrödinger-Maxwell方程非线性基态解变分法临界点理论Nehari流形
Schrödinger-Maxwell equationsnonlinearground state solutionvariational methodscritical point theoryNehari manifold
《数学杂志》 2018 (4)
743-750,8
广西自然科学基金资助 (2015GXNSFBA139018) 广西师范大学科学研究基金资助(2014ZD001)广西师范大学研究生创新项目基金资助(XYCZ2017074).
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