Multiplicity results for non-homogeneous differential equations

This paper investigates the existence of infinitely many weak solutions for a class of anisotropic elliptic equations governed by non-homogeneous differential operators that extend both the Laplacian and mean curvature operators. By introducing and working under novel assumptions, we establish these results using a powerful variational principle developed by B. Ricceri. Our approach demonstrates how generalized operators can accommodate a broader range of anisotropic conditions, contributing to the advancement of variational methods in the study of elliptic equations. The findings provide a deeper understanding of solution multiplicity in non-linear frameworks, expanding current theoretical results in the field.