This paper is concerned with the Dirichlet problem of the asymptotically linear wave equation (t, x, u) in a n-dimensional ball with radius R, where n > 1 and g (t, x, u) is radially symmetric in x and T -periodic in time. An interesting feature is that the solvable of the problem depends on the space dimension n and the arithmetical properties of R and T . Based on the spectral properties of the radially symmetric wave operator, we use the saddle point reduction and variational methods to construct at least three radially symmetric solutions with time period T , when T is a rational multiple of R and g(t, x, u) satisfies some monotonicity and asymptotically linear 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.