On the least energy solutions for semilinear Schrödinger equation with electromagnetic fields involving critical growth and indefinite potentials
On the least energy solutions for semilinear Schrödinger equation with electromagnetic fields involving critical growth and indefinite potentials
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DOI：
10.1080/00036811.2017.1359559
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发表时间：
2018-09
影响因子：
1.1
通讯作者：
Y. Jiao;Z. Tang
中科院分区：
文献类型：
--
作者：
Y. Jiao;Z. Tang
本文研究了具有临界增长的电磁场的半线性薛定谔方程，其中，且其零点集不为空，是临界Sobolev指数，是一个常数使得算子可能是不定的但非退化的。利用变分方法和修正的Nehari-Pankov方法，证明了该方程存在一个能量最小的解，该解局限于势阱附近。我们在这里得到的结果扩展了薛定谔方程，其中涉及临界增长，但不涉及电磁场的相应结果。
Abstract In this paper, we are concerned with the following semilinear Schrödinger equation with electromagnetic fields and critical growth for sufficiently large , where , and its zero set is not empty, is the critical Sobolev exponent, is a constant such that the operator might be indefinite but is non-degenerate. Using variational method and modified Nehari–Pankov method, we prove the equation admits a least energy solution which localizes near the potential well . The results we obtain here extend the corresponding results for the Schrödinger equation which involves critical growth but does not involve electromagnetic fields.