It is well known that the problem of estimating the state and parameters of discrete-time nonlinear dynamic systems from noisy measurements can be formulated as a nonlinear two-point boundaryvalue problem. In this paper, an algorithm is developed for solving the above boundary-value problem. The algorithm, which is based on Newton's method, requires very little storage. A detailed discussion of...

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundaryvalue problem −∆u = a(x)u in D, lim |x|→1 u(x) = lim |x|→∞ u(x) = 0. Here D is the complement of the closed unit ball of Rn (n ≥ 3), σ < 1 and the function a is a nonnegative function in C loc(D), 0 < γ < 1, satisfying some appropriate assumptions r...

Directional emission from a slit surrounded by rectangular grooves on the exit surface in a conducting plane is investigated. An electromagnetic boundaryvalue problem dealing with a slit surrounded by rectangular grooves on the exit surface in a conducting plane is rigourously solved based on the Fourier transform, eigenfunction expansion, and mode-matching method. The radiation pattern from th...