We perform an weighted Sobolev space approach to prove a Trudinger-Moser type inequality in the upper half-space. As applications, we derive some existence and multiplicity results for the problemunder some technical condition on a, b and the the exponential nonlinearity f . The ideas can also be used to deal with Neumann boundary conditions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.