Existence, Non‐Existence, and Uniqueness of Solutions for a Generalized Fractional <i>p</i> ‐Kirchhoff Equation

ABSTRACT This paper investigates the existence and non‐existence and uniqueness of global solutions for certain parameter values in a new class of generalized fractional ‐Kirchhoff equations in the whole space. Using the Pohozaev and Nehari identities for an auxiliary problem, together with the fractional Gagliardo–Nirenberg inequality and the concentration–compactness principle, we prove that all optimizer solutions to the auxiliary problem are, in fact, unique minimizer solutions to the original problem.