We introduce the notion of formally self-adjoint conformally covariant polydifferential operators and give some constructions families such operators. In one direction, we show that any homogeneous variational scalar Riemannian invariant (CVI) induces these another use ambient metric to alternative certain produced this way, which is a self-adjoint, fourth-order, tridifferential operator should...

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of...

This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of the classical Hankel integral transform. These results are based upon the properties of the classical Bessel and Laguerre second-order differential equations...

Abstract The connection between the number of internal zeros nontrivial solutions to fourth-order self-adjoint boundary value problems and inertia index these is studied. We specify types for which such a can be established. In addition, we derivatives Examples demonstrating effectiveness proposed new approach an oscillatory problem are considered.

A linear completely nonhomogeneous generally nonlocal multipoint problem is investigated for a fourth-order differential equation with generally nonsmooth coefficients satisfying some general conditions such as pintegrability and boundedness. A system of five integro-algebraic equations called an adjoint system is introduced for this problem. A concept of a Green functional is introduced as a s...

By h(G, x) and P (G, λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fourth character R4(G), is given in this paper. Using the properties of the adjoint polynomials, the adjoint equivalence class of graph Bn−6,1,2 is determined, which can be regarded as the continuance of the paper written by Wang et al. [J. Wan...