(untitled) (Analysis in Theory and Applications, 2025)
This paper study a general nonlocal problem characterized by the equation: \[ -L_K u + V(x)u = P(x)h(u) \] in R. Here, L_K represents a nonlocal integro-differential operator, and h is a nonlinear term displaying subcritical or critical growth of Trudinger-Moser type. We initially prove the existence of a ground state solution by employing variational methods and innovative analytical approaches. Furthermore, through the application of constrained variational methods, Brouwer degree theory, and a quantitative deformation lemma, we establish the existence of a sign-changing solution with minimal energy, surpassing the energy of the ground state solution.