Existence and Concentration of Positive Ground State Solutions for a (P, Q)-Kirchhoff Type Equation With Moser-Trudinger Nonlinearity

In this work, we concern the existence and concentration of positive ground state solutions for the following (p, q) -Kirchhoff type problem \array{ll - (1+aₑ₍| u|ᵖdx) ₚ u- (1+bₑ₍| u|qdx) q u+V (x) (|u|^p-2u+|u|^q-2u) \ \\ =f (u) in\, RN, \, u W^1, p (RN) W^1, q (RN), u>0 \, \, in\, \, RN, array. where >0 is a small parameter, a, b>0, 1m-Laplacian operator, the potential V: RN R is a positive continuous function and f: R R is a continuous nonlinearity involving critical exponential growth and not satisfying usual Ambrosetti-Rabinowitz condition. The existence and concentration behavior of positive ground state solutions are established by variational methods combined with some sharp exponential type inequalities.