Authors: A. R. ALIEV, N. L. MURADOVA

Abstract. In the paper, we consider a fourth-order operator-differential equation on the entire axis, the main part of which has a multiple characteristic, and we introduce the concept of its "smoothly" regular solvability. We find exact values of the norms of intermediate derivatives operators in a Sobolev-type space and indicate their connection with the conditions for the solvability of the equation under study. Note that the conditions found for "smoothly" regular solvability are sufficient and are imposed only on the operator coefficients of the operator-differential equation under consideration.

Keywords: operator-differential equation, smooth solution, self-adjoint operator, Hilbert space, intermediate derivative operators

DOI:  https://doi.org/10.32010/j.bmj.2022.01

Authors: A. R. ALIEV, N. L. MURADOVA

Abstract. In the paper, we consider a fourth-order operator-differential equation on the entire axis, the main part of which has a multiple characteristic, and we introduce the concept of its "smoothly" regular solvability. We find exact values of the norms of intermediate derivatives operators in a Sobolev-type space and indicate their connection with the conditions for the solvability of the equation under study. Note that the conditions found for "smoothly" regular solvability are sufficient and are imposed only on the operator coefficients of the operator-differential equation under consideration.

Keywords: operator-differential equation, smooth solution, self-adjoint operator, Hilbert space, intermediate derivative operators

DOI:  https://doi.org/10.32010/j.bmj.2022.01

Authors: A. R. ALIEV, N. L. MURADOVA

Abstract. In the paper, we consider a fourth-order operator-differential equation on the entire axis, the main part of which has a multiple characteristic, and we introduce the concept of its "smoothly" regular solvability. We find exact values of the norms of intermediate derivatives operators in a Sobolev-type space and indicate their connection with the conditions for the solvability of the equation under study. Note that the conditions found for "smoothly" regular solvability are sufficient and are imposed only on the operator coefficients of the operator-differential equation under consideration.

Keywords: operator-differential equation, smooth solution, self-adjoint operator, Hilbert space, intermediate derivative operators

DOI:  https://doi.org/10.32010/j.bmj.2022.01

Authors: A. R. ALIEV, N. L. MURADOVA

Abstract. In the paper, we consider a fourth-order operator-differential equation on the entire axis, the main part of which has a multiple characteristic, and we introduce the concept of its "smoothly" regular solvability. We find exact values of the norms of intermediate derivatives operators in a Sobolev-type space and indicate their connection with the conditions for the solvability of the equation under study. Note that the conditions found for "smoothly" regular solvability are sufficient and are imposed only on the operator coefficients of the operator-differential equation under consideration.

Keywords: operator-differential equation, smooth solution, self-adjoint operator, Hilbert space, intermediate derivative operators

DOI:  https://doi.org/10.32010/j.bmj.2022.01