An asymptotically periodic and asymptotically linear Schrodinger equation with indefinite linear part

作者：Lin, Xiaoyan^*; Tang, Xianhua

来源：Computers & Mathematics with Applications, 2015, 70(4): 726-736.

DOI：10.1016/j.camwa.2015.06.013

• Schrodinger equation
• Asymptotically periodic
• Asymptotically linear
• Sign-changing potential

We consider the semilinear Schrodinger equation
{-Delta u + V(x)u = f(x,u), x is an element of R-N, u is an element of H-1(R-N),
where V(x) is asymptotically periodic and sign-changing,f(x, u) is asymptotically periodic in x, and asymptotically linear as vertical bar u vertical bar -> infinity. Under some weak assumptions on V and f, we prove that the above problem has a nontrivial solution.

• 出版日期2015-8
• 单位怀化学院; 中南大学