Narrow Results

Analyzes has been carried out for the two-dimensional whooping cough model. The solution of the arising nonlinear initial/boundary value problem is computed by a homotopy analysis method (HAM). Convergence of the derived solution is highlighted. The plotted graphs show great confidence into the used methodology of solution.

In this paper, the limit behavior of nonlinear problems with nonhomogeneous Fourier boundary conditions, in a connected domain is established. This domain consists of two separate parts jointed by a set of bridges. The parameter describing the heterogeneities of the material and the size of the bridges can be very small. The homogenization method is used to estimate the field of temperatures attainable in the medium, depending of the relative order of the size of the bridges. Three situations are studied according to the connectedness of the components of the domain.

This work deals with the existence of at least one positive ground state solution for a stationary perturbed critical elliptic system with superlinear potential. Our problems involve the critical Sobolev constants which generate the lack of compactness in unbounded domains; we overcome such difficulty by using the concept of the Palais–Smale convergence. We make recourse to the Ekeland variational principle to show that our problem has a positive time-independent solution with positive energy as the total energy of the system.