CONCENTRATING NORMALIZED SOLUTIONS FOR 2D NONLOCAL SCHRÖDINGER EQUATIONS WITH CRITICAL EXPONENTIAL GROWTH

We study the existence of solutions to nonlocal Schrödinger problems with different types of potentials (formula present) is known as the Lagrange multiplier, κ > 0 is a parameter, W ∈ C(R2) is the nonnegative external potential, μ ∈ (0, 2), and F denotes the primitive function of f ∈ C(R) which has critical exponential growth in the Trudinger-Moser sense at infinity. We prove that the problems admit at least a positive solution, and we analyze the concentrating behavior.