We apply a method of quasilinearization to a boundary value problem for an ordinary differential equation on an unbounded domain. A uniquely determined Green’s function, which is integrable and of fixed sign, is employed. The hypotheses to apply the quasilinearization method imply uniqueness of solutions. The quasilinearization method generates a bilateral iteration scheme in which the iterates...

This paper is devoted to the valuation of American multi-asset put options. It is well known that the American multi-asset put option satisfies a linear complementary problem (LCP) on an unbounded domain. We consider a penalty method in which the LCP could be reformulated into a nonlinear parabolic problem on an unbounded domain. For the unbounded computational domain, a perfectly matched layer...

We prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. The data prescribed is the rearrangement class of the vorticity field. The corresponding stream function satisfies a semilinear elliptic partial differential equation. The result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...

We consider three types of semilinear second order PDEs on a cylindrical domain Ω × (0,∞), where Ω is a bounded domain in N , N 2. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × (0,∞) is reserved for time t, the third type is an elliptic equation with a singled out unbounded variable t. We discuss the asymptotic behavior, as t ...

Infinite product formulae for conformally mapping an unbounded multiply connected circle domain to an unbounded canonical radial or circular slit domain, or to domains with both radial and circular slit boundary components are derived and implemented numerically and graphically. The formulae are generated by analytic continuation with the reflection principle. Convergence of the infinite produc...

We present an extension of the classical testing semantics for the case when nondeterminism is unbounded. We deene the corresponding may and must preorders in the new framework. As in the bounded setting the may preorder can be characterized by using the set of nite traces of processes. On the contrary, in order to characterize the must preorder is necessary to record some additional informatio...

In this paper, we study the boundedness of pseudo-differential operators with symbols in Sm ρ,δ on the modulation spaces M p,q. We discuss the order m for the boundedness Op(Sm ρ,δ) ⊂ L(M p,q(Rn)) to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space Mp,q with q 6= 2. This unboundedness is still true even if we assume a generalized T...