On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients

On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients

On Linear Singular Functional-differential Equations in One Functional Space

The case where K and S are continuous on Lp[0,1] operators is well studied (see, e.g., [1] and the references therein). Here we suppose that the functions K(t,s) and B(t) may be nonintegrable at t = 0. More precisely, we will formulate conditions on operators K and S in Sections 2 and 3. Under such conditions, those operators are not bounded on L[0,1] and one has to choose other functional spac...

Liouvillian Solutions of Linear Differential Equations with Liouvillian Coefficients

Let L(y) = b be a linear differential equation with coefficients in a differential field K. We discuss the problem of deciding if such an equation has a non-zero solution in K and give a decision procedure in case K is an elementary extension of the field of rational functions or is an algebraic extension of a transcendental liouvillian extension of the field of rational functions. We show how ...

A Uniqueness Result on Ordinary Differential Equations with Singular Coefficients

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the order of singularities of the coefficients and provide examples to illustrate the results. 1. Results and examples Classical results on the existence and uniqueness of ordinary differential equations are mostly concerned with continuous coeffici...

On Periodic Solutions of Systems of Linear Functional Differential Equations

This paper deals with the system of functional-diierential equations dx(t) dt = p(x)(t) + q(t); where p : C!(R n) ! L!(R n) is a linear bounded operator, q 2 L!(R n), ! > 0 and C!(R n) and L!(R n) are spaces of n-dimensional !-periodic vector functions with continuous and integrable on 0;!] components, respectively. Conditions which guarantee the existence of a unique !-periodic solution and co...