Nehari Type Ground State Solutions for Asymptotically Periodic Schrodinger-PoissonSystems

作者：Chen, Sitong; Tang, Xianhua^*

来源：Taiwanese Journal of Mathematics, 2017, 21(2): 363-383.

DOI：10.11650/tjm/7784

• THOMAS-FERMI
• EQUATIONS
• ATOMS
• SUPER

This paper is dedicated to studying the following Schrodinger-Poisson system { -Delta u + V(x)u+K(x)phi(x)u= f(x,u), x epsilon R-3 -Delta phi = K(x)u(2), x epsilon R-3, where V(x), K(x) and f(x,u) are periodic or asymptotically periodic in x. We use the non-Nehari manifold approach to establish the existence of the Nehari type ground state solutions in two cases: the periodic one and the asymptotically periodic case, by introducing weaker conditions lim(|t|->infinity) (f(0)(t) f(x,s)ds) /|t|(3) = infinity uniformly in x epsilon R-3 and @@@ [f(x,T)/T-3-f(x,tr)/(t Gamma)(3)] sign(1 - t) + theta V-0(x)|1-t(2)|/(t Gamma)(2) >= 0, for all x epsilon R-3, t > 0, T not equal 0 @@@ with constant theta(0) epsilon (0,1), instead of lim (|t|)->infinity (f(0)(t) f(x, s)ds) /|t|(4)=infinity uniformly in x epsilon R-3 and the usual Nehari-type monotonic condition on f(x,t) /|t|(3).

• 出版日期2017
• 单位中南大学