On regularized trace formulas for a well-posed perturbation of the m-Laplace operator

Spectral properties of the iterated Laplacian with a potential in a punctured domain

“…In this section we repeat the results of the paper [7]. However, here we formulate them also for the case d ≤ 2m.…”

“…In this paper we observe that the results of the work [7] are valid, even when there is a potential and, the spatial dimension is greater than two.…”

“…Now, we are in a way in the Hilbert space H 2 (D) to introduce an operator associated with the differential equation 1, that is, (−∆) m u + qu. We denote by K M the operator defined as Discussing as in the works [5,7,8], we get the following statements:…”

To the Question of a Multipoint Mixed Boundary Value Problem for a Wave Equation

“…Using this fact, let us prove solvability of the problem (1)- (3). The solution of the problem (1)-(3) we will seek in the view , ∑ ∑ ,…”

“…It is well known that some problems in mechanics and physics lead to partial differential equations of the hyperbolic type. When posed, the task sometimes lacks the classical boundary condition and the need arises to have a nonlocal boundary condition (see, [2,3,4,5]). A simple example of such nonlocal conditions are multipoint conditions relating the value of the solution at the boundary points with the values at some interior points.…”