Two-Point Problem for Higher-Order Systems

On Two-point Boundary Value Problems for Systems of Higher-order Ordinary Differential Equations with Singularities

The sufficient conditions of solvability and unique solvability of the two-point boundary value problems of Vallèe-Poussin and Cauchy-Niccoletti have been found for a system of ordinary differential equations of the form u(n) = f(t, u, u′, . . . , u(n−1)), where the vector function f :]a, b[×Rnl → Rl has nonintegrable singularities with respect to the first argument at the points a and b. § 1. ...

Two - point higher order BVPs with singularities in phase variables ∗

The existence of solutions for singular higher order differential equations with the Lidstone or the (n, p) boundary conditions is proved. The righthand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities. Proofs are based on the method of a priori estim...

Two Session Typing Systems for Higher-Order Mobile Processes

This paper proposes two typing systems for session interactions in higherorder mobile processes. Session types for the HOπ-calculus capture high-level structures of communication protocols and code mobility as type abstraction, and can be used to statically check the safe and consistent process composition in communication-centric distributed software. Integration of arbitrary higher-order code...

Tarski's Fixed-Point Theorem and Higher-Order Term Rewrite Systems

Solvability of a third-order two-point boundary value problem

A new comparison theorem is proved and then used to investigate the solvability of a third-order two-point boundary value problem  u′′′(t) + f(t, u(t), u′(t), u′′(t))) = 0, u(0) = u′(2π) = 0, u′′(0) = u′′(2π). Some existence results are established for this problem via upper and lower solutions method and fixed point theory. 2000MR Subject Classification: 34B15, 34C05