Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (4): 651-655.

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Ground State Solutions for A Periodic Schrödinger Equation with Critical Sobolev Exponent

Xu Na, Ma Shiwang   

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071
  • Received:2014-03-28 Revised:2014-10-21 Online:2015-08-25 Published:2015-08-25

Abstract:

In this note, we obtain the existence of ground state solutions for the following periodic Schrödinger equation
u +V(x)u=K(x)|u|2*-2 u+g(x,u), uH1(RN),
where N≥ 4 and 2*=(2N)/(N-2) is the critical Sobolev exponent. Our result is a complement to some recent works concerning the existence of ground state solutions of the above equation.

Key words: Ground state solution, Critical Sobolev exponent, Linking

CLC Number: 

  • O175.25
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