Nonexistence and Existence of Solutions with Prescribed Norms for Nonlocal Elliptic Equations with Combined Nonlinearities

In this paper, we study the nonlocal equation (Formula presented.), (Formula presented.) having a prescribed mass (Formula presented.) where (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), c is a positive constant, p, (Formula presented.) with (Formula presented.) and (Formula presented.). This research is meaningful from a physical point of view. Using variational methods, we present some results on the nonexistence and existence of solutions under different cases p and q which improve upon the previous ones via topological theory.