Critical logarithmic double phase problems of Brezis–Nirenberg type with nonlinear boundary condition

Abstract In this paper, we investigate the existence and multiplicity of solutions to a class of nonlinear elliptic problems governed by the logarithmic double phase operator and subject to nonlinear critical Neumann boundary conditions. By employing variational methods in combination with topological tools such as truncation techniques and Krasnosel’skii’s genus theory, we establish the existence of infinitely many weak solutions with negative energy sign. The results highlight the rich solution structure arising from the interplay between the logarithmic double phase operator and the critical boundary growth.