We establish sufficient conditions for the existence of a unique critical point for the solution to the semi linear elliptic problem ∆u = f(u)+w with zero Dirichlet boundary condition.

We derive a closed form expression for the Green function of linear evolution equation with the Dirichlet boundary condition for an arbitrary region, based on singular perturbation approach to boundary problems. PACS numbers: 03.65.-w, 03.65.Ge, 02.90.+p Published in Journal of Physics A: Mathematical and General Vol. 32 (1999) 1261-1267 e–mails: [email protected], [email protected] 1

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the A−amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl m−function associated with the Schrödinger operator H = −∂2 x + q (x) on L2 (0,∞) with Dirichlet boundary condition at x = 0.

This paper presents a simple and systematic way for imposing boundary conditions in the differential quadrature free and forced vibration analysis of beams and rectangular plates. First, the Dirichlet- and Neumann-type boundary conditions of the beam (or plate) are expressed as differential quadrature analog equations at the grid points on or near the boundaries. Then, similar to CBCGE (direct ...

It is proved that the scattering amplitude known at a fixed frequency, a fixed direction of the incident plane wave and all directions of the scattered wave in a solid angle, however small, determine uniquely the shape of a strictly convex obstacle with a smooth but not analytic boundary on which the Dirichlet boundary condition is assumed.

The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green’s function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.

We prove the existence of strong solution for Blake & Zisserman functional under Dirichlet boundary condition. The result is obtained by showing partial regularity of weak solutions up to the boundary through blow-up technique and a decay property for bi-harmonic functions in half disk.

The initial-boundary value problem for a linear parabolic equation with the Dirichlet boundary condition is solved approximately by applying the finite element discretization in the space dimension and three types of finite-difference discretizations in time: the backward, the Crank-Nicolson and the Calahan discretization. New error bounds are derived.

We prove the existence and uniqueness of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with Dirichlet boundary condition for large anisotropies and small domains, where the domains are non-simply connected.

We study the equation−∆pu+|x||u|u = |x|b|u|q−2u with Dirichlet boundary condition on B(0, R) or on R . We prove the existence of the radial solution and nonradial solutions of this equation.