Ground state sign-changing solutions for a class of nonlinear fractional Schrodinger-Poisson system in R3

摘要

In this paper, we are concerned with the existence of the least energy sign-changing solutions for the following fractional Schrodinger-Poisson system: disp-formula id="Equ36"mml:mtable mml:mtrmml:mtd columnalign="right"mml:mfenced open="{"mml:mtable mml:mtr mml:mtd mml:mtd mml:mtd columnalign="left(-Delta )su+V(x)u+lambda phi (x)u=f(x,u),mml:mspace width="1em"mml:mspace mml:mtd mml:mtd columnalign="right"in mml:mspace width="0.166667em" mml:mspace mml:mspace width="4pt"mml:mspace R3,mml:mtd mml:mtr mml:mtrmml:mtd columnalign="right mml:mtd mml:mtd columnalign="left"(-Delta )t phi =u2,mml:mtd mml:mtd columnalign="right in mml:mspace width="0.166667em" mml:mspace mml:mspace width="4pt mml:mspace>R3,mml:mtd mml:mtr mml:mtable mml:mfenced mml:mtd mml:mtr mml:mtable disp-formula>where lambda is an element of R+ is a parameter, s,t is an element of (0,1) and 4s+2t>3, (-Delta )s stands for the fractional Laplacian. By constraint variational method and quantitative deformation lemma, we prove that the above problem has one least energy sign-changing solution. Moreover, for any lambda 0, we show that the energy of the least energy sign-changing solutions is strictly larger than two times the ground state energy. Finally, we consider lambda as a parameter and study the convergence property of the least energy sign-changing solutions as lambda SE arrow 0.