The conjugate of a singular functional differential operator

The Theory of Singular Differential-Operator Equations

We consider methods of reduction of differential operator equations with the Fredholm operator in the main expression to regular problems. Relation between the initial conditions choice problem and the Jordan structure of operator coefficients of equations is shown. The theorem of existence and uniqueness of the initial problem is proved. The method of fundamental operators is used for construc...

Inverse problem for a singular differential operator

In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt's theorem concerning the structure of the difference q(x) − ˜ q(x) for the singular Sturm Liouville problem defined on the finite interval (0, π) having the singularity type 1 4 sin 2 x at the points 0 and π.

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...

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...

A Method to Estimate the Solution of a Weakly Singular Non-linear Integro-differential Equations by Applying the Homotopy Methods