We prove the correctness of the conditional boundary value problem for an operator differential equation of the fourth order. A priori estimate is get. Uniqueness and conditional stability of solution are proved. The approximate solution is construct and get estimates of the norm of the difference between the exact and approximate solution.
1. Levine H.A. Logarithmic Convexity and the Cauchy Problem for some Abstract Second order Differential Inequalities. Journal of Dif. Equations, 1970, V.8, pp.34–55.
2. Krein S.G. Linear differential equations in a Banach space. M.: Nauka, 1967.
3. Pyatkov S.G. Properties of the functions of a spectral problem and some of their applications. Some applications of functional analysis to problems of mathematical physics: Sat. scientific. tr.USSR Academy of Sciences. Sib. Dep-set. Institute of Mathematics. Novosibirsk, (1986), pp.65–84.
4. Fayazov K.S. Ill-posed Cauchy problem for differential equations of first and second order with operator coefficients. Siberian Mathematical Journal, 1994, V. 35, No. 3, pp.702–706.
5. Kislov N.V. Nonhomogeneous boundary value problems for operator-differential equations of mixed type and their applications. Math. USSR-Sb., 1986, V. 53, No. 1, pp.17–35.
6. Egorov I.E., Pyatkov S.G., Popov S.V. Nonclassical differential-operator equations. Nauka, Novosibirsk, 2000.
7. Kabanikhin S.I. Inverse and ill-posed problems. Monograph, Siberian Scientific Publishing House, 2008.
Fayazov, Kudratillo; Khajiev, Ikrom; and Fayazova, Z.
"Ill-posed boundary value problem for operator-differential equation of fourth order,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 1:
2, Article 3.