Kirchhoff Equations with Choquard Exponential Type Nonlinearity Involving the Fractional Laplacian

In this article, we deal with the existence of non-negative solutions of the class of following non local problem {-M(integral(Rn)integral(Rn) | u(x)- u(y)|(n/s)/ |x - y|(2n) dxdy) (- Delta)(n/s)(s) u = (integral(Omega) G(y, u)/|x - y|(mu) dy) g(x, u) in Omega, u = 0 in R-n\Omega, where (-Delta)(n/s)(s) is the n/s-fractional Laplace operator, n >= 1, s is an element of (0, 1) such that n/s >= 2, Omega subset of R-n is a bounded domain with Lipschitz boundary, M : R+ -> R+ and g : Omega x R -> R are continuous functions, where g behaves like exp(|u|(n/n-s)) as |u| -> infinity. The key feature of this article is the presence of Kirchhoff model along with convolution type nonlinearity having exponential growth which appears in several physical and biological models.