Existence and concentration of normalized solutions for p-Laplacian equations with logarithmic nonlinearity

We investigate the existence and concentration of normalized solutions for a p-Laplacian problem with logarithmic nonlinearity of type \ \ array{ll -ᵖₚ u+V (x) |u|^p-2u= |u|^p-2u+|u|^p-2u|u|ᵖ ~in~ RN, ₑ₍|u|ᵖdx=aᵖN, array. \ where a, > 0, R is known as the Lagrange multiplier, ₚ =div (| |^p-2) denotes the usual p-Laplacian operator with 2 p < N and V C⁰ (RN) is the potential which satisfies some suitable assumptions. We prove that the number of positive solutions depends on the profile of V and each solution concentrates around its corresponding global minimum point of V in the semiclassical limit when 0^+ using variational method. Moreover, we also get the existence of normalized solutions for some logarithmic p-Laplacian equations involving mass-supercritical nonlinearities.