Some properties of logarithmic p-Laplace operators and applications

A study of the existence and uniqueness of the weak solution to a class of nonlinear elliptic equations governed by the logarithmic perturbation is offered.We exploit interesting properties of the new modular function involving L p log L -growth and the optimal embedding theorem for Orlicz-Sobolev spaces.We are concerned with these properties in analyzing the existence and uniqueness of the solution by the theory of pseudo-monotone operators proposed in [2, 3] combined with variational methods.Our approach deals not only with problems of the p -Laplacian type but also yields a slight extension of the results for more general differential operators with a similar structure.