On Lyapunov-type inequalities for a certain class of partial differential equations

A Lyapunov-type inequality is established for the partial differential equation:(Formula presented.) where (Formula presented.), (Formula presented.), a<b, (Formula presented.) is an open bounded subset in (Formula presented.), (Formula presented.), (Formula presented.) is the differential operator given by (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.). Next, some sign-changing criteria are obtained for the nontrivial solutions to the considered problem. © 2018 Informa UK Limited, trading as Taylor & Francis Group