Multiple Positive Bound State Solutions for Fractional Schrodinger-Poisson System with Critical Nonlocal Term

For the fractional Schrodinger-Poisson system with nonlocal critical exponent { (-Delta)(s)u + (V(x) + lambda)u = phi|u|(2)*(s -3) u, x is an element of R-3, (-Delta)(s) phi = vertical bar u vertical bar(2*s) (-1), x is an element of R-3, where s is an element of (1/2, 3/4), 2*(s) = 6/3-2s is the fractional critical Sobolev exponent and V( x) is an element of L-3/2s (R-3) is a nonnegative potential, combining with Variational methods and Brouwer degree theory, we investigate the existence and multiplicity of positive bound solutions if lambda > 0 is small. These results extend and improve some recent works with nonlocal critical exponent.

Automated summary

In this study, the existence and multiplicity of positive bound solutions for the fractional Schrodinger-Poisson system with nonlocal critical exponent are investigated using variational methods and Brouwer degree theory. These results extend and improve upon recent works with nonlocal critical exponent, and are focused on the case where λ > 0 is small.