Clustered solutions around harmonic centers to a coupled elliptic system
As a model for elliptic boundary value problems, we consider the Dirichlet problem for an elliptic operator. Solutions have singular expansions near the conical points of the domain. We give formulas for the coefficients in these expansions.
We study oscillatory solutions of semilinear first order symmetric hyperbolic system , with real analytic .The main advance in this paper is that it treats multidimensional problems with profiles that are almost periodic in with only the natural hypothesis of coherence.In the special case where has constant coefficients and the phases are linear, the solutions have asymptotic descriptionwhere the profile is almost periodic in .The main novelty in the analysis is the space of profiles which...
We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over , and prove that it is described by a maximal compact attractor in .
In this paper, we obtain some existence theorems of nonnegative solutions with compact support for homogeneous Dirichlet elliptic problems; we also extend these results to parabolis systems.Supersolution and comparison principles are our main ingredients.