A logarithmic Schrödinger equation with asymptotic conditions on the potential
A logarithmic Schrödinger equation with asymptotic conditions on the potential
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DOI：
10.1016/j.jmaa.2015.11.071
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发表时间：
2015-10
影响因子：
1.3
通讯作者：
Chao Ji;A. Szulkin
中科院分区：
文献类型：
--
作者：
Chao Ji;A. Szulkin
本文考虑一类具有可变号势的对数薛定谔方程。当势是强制势时，我们利用喷泉定理的某些参数得到了无穷多个解;当势是有界势时，我们得到了基态解，即具有最小可能能量的非平凡解.相应的泛函是一个光滑项和一个凸下连续项之和。
In this paper we consider a class of logarithmic Schrödinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions by adapting some arguments of the Fountain theorem, and in the case of bounded potential we obtain a ground state solution, i.e. a nontrivial solution with least possible energy. The functional corresponding to the problem is the sum of a smooth and a convex lower semicontinuous term.