A class of solvable second-order ordinary differential equations with variable coefficientsAbstract. This paper is devoted to the existence and compactness of the resolvent and the discreteness of the spectrum of non-semibounded differential operators.
This paper is devoted to the existence, smoothness and approximative properties of solutions of the semiperiodical Dirichlet problem of a class of nonclassical type degenerate nonlinear equations.
Partial differential equations of the third order are the basis of mathematical models of many phenomena and processes, such as the phenomenon of energy transfer of hydrolysis of adenosine triphosphate molecules along protein molecules in the form of solitary waves, i.e. solitons, the process of transferring soil moisture in the aeration zone, taking into account its movement against the moisture potential. In particular, this class includes the nonlinear Korteweg-de Vries equation, which is the main equation of modern mathematical physics. It is known that various problems have been studied for the Korteweg-de Vries equation and many fundamental results obtained. In this paper, issues about the existence of a resolvent and separability (maximum smoothness of solutions) of a class of linear singular operators of the Korteweg-de Vries type in the case of an unbounded domain with strongly increasing coefficients are investigated.
In this paper, for a class of third-order differential operators, we study the existence of the resolvent and the separability of the operator. In this paper, under certain restrictions on the coefficients, the existence of a resolvent is proved and a condition is found that ensures the separability of the operator
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