In 2018, according to the approved plan, the department conducts 11 research works on the topic “Unambiguous solutions of problems of mathematical physics and qualitative properties of solutions.”<\/p>\n
Work 1: \u201dInvestigation of the negative spectrum of quasi-elliptic operators\u201d.
\nExecutor: corr-member of ANAS, prof. R.V. Huseynov.
\nDuring the reporting period, the spectrum for elliptic and some quasi-elliptic equations of high order was investigated. In particular, analogues of the stationary Schr\u00f6dinger operator of high order are studied. In this case, a negative spectrum was considered for different types of differential operator and a given potential Q (x). We investigated what necessary conditions must be imposed on the potential, that the negative spectrum be finite and infinite.
\nWork 2: \u201dAn approximate solution of an inverse problem for a semilinear elliptic equation\u201d.
\nExecutor: prof. A.Ya. Akhundov.
\nThe inverse problem of determining the unknown coefficients on the right-hand side of the system of elliptic equations is investigated. The problem is solved by the method of successive approximations, the convergence of the approximate solution to the exact solution is proved, with the speed of the geometric series, the theorem on the existence, uniqueness, and stability of the solution is proved.<\/p>\n