On Solvability of Integro-Differential Equations

Nonlinear Integro - Differential Equations

On the Solvability of Magnetic Differential Equations

The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type ~ B ·∇Φ = s. We apply the necessary and sufficient criterion for the existence of the potential Φ and find that a static equilibrium configuration of a magnetically confined plasma does not exist in axi-symmetric toroidal geometry. AMS classification...

On d-solvability for linear differential equations

The aim of this paper is to investigate the possibility of solving a linear differential equation of degree n by means of differential equations of degree less than or equal to a fixed d, 1 ≤ d < n. This paper recovers and extends work of G. Fano, M. F. Singer and E. Compoint. Representations of algebraic Lie algebras are themain tool. © 2008 Elsevier Ltd. All rights reserved.

Singular perturbations of integro-differential equations

We study the singular perturbation problem (E2) 2 2u′′ 2 (t) + u ′ 2(t) = Au2(t) + (K ∗Au2)(t) + f2(t), t ≥ 0, 2 > 0, for the integrodifferential equation (E) w′(t) = Aw(t) + (K ∗Aw)(t) + f(t), t ≥ 0, in a Banach space, when 2 → 0. Under the assumption that A is the generator of a strongly continuous cosine family and under some regularity conditions on the scalar-valued kernel K we show that p...

Positive Solutions of Volterra Integro–differential Equations

We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and ...