On the Neumann problem with combined nonlinearities

On Nonlinear Dirichlet–Neumann Algorithms for Jumping Nonlinearities

We consider a quasilinear elliptic transmission problem where the nonlinearity changes discontinuously across two subdomains. By a reformulation of the problem via Kirchhoff transformation we first obtain linear problems on the subdomains together with nonlinear transmission conditions and then a nonlinear Steklov– Poincaré interface equation. We introduce a Dirichlet–Neumann iteration for this...

Dependence on Parameters for the Dirichlet Problem with Superlinear Nonlinearities

The nonlinear second order differential equation d dt h(t, x′(t)) + g(t, x(t)) = 0, t ∈ [0, T ] a.e. x′(0) = x′(T ) = 0 with superlinear function g is investigated. Based on dual variational method the existence of solution is proved. Dependence on parameters and approximation method are also presented.

The Neumann Problem on Lipschitz Domains

Au — 0 in D; u = ƒ on bD9 where ƒ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. Calderón et al. [1]. For dimension 2, see (d) below. In [4] and [5] we found an elementary integral formula (7) and used it to prove a theorem of Dahlberg (Theorem 1) on Lipschitz domains. Unknown to us, this formula had already been discovered long ago by Payne and We...

On the Von Neumann Economic Growth Problem

A Boundary Meshless Method for Neumann Problem

Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...