Degeneracy and Bi–Nonlocal Effects in Weighted Quasilinear Elliptic Problems: Existence of Multiple Weak Solutions

ABSTRACT This manuscript addresses the multiplicity of weak solutions for a weighted elliptic problem in a domain , where , involving a degenerate ‐Laplace operator with a coefficient that controls the degeneracy. The equation includes two nonlocal terms, characterized by nonlinear functions and , each coupled with integrals over . The goal is to establish the existence of at least three weak solutions under general growth conditions for the nonlinearities. Critical point theory and variational methods are employed to prove the existence of nontrivial solutions for specific parameter ranges. These results extend previous work by incorporating the degeneracy of the operator, the nonlocal terms, and the growth behaviors of the nonlinearities, particularly in higher dimensions.