Solving of the Fourth Order Differential Equations with the Neumann Problem
In this paper we considered the Neumann problem for
the fourth order differential equation. First we define the weighted Sobolev space
2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution,
as well as give the description of the spectrum and of the domain of definition of the corresponding operator.
[1] A. A. Dezin, Degenerate Operator Equations, Mat. Sbornik, vol. 43, no.
3, pp. 287 - 298, 1982 [in Russian].
[2] A. A. Dezin, Partial Differential Equations (An Introduction to a General
Theory of Linear Boundary Value Problems), Springer, 1987.
[3] L. Tepoyan, Degenerate Fourth-Order Differential-Operator Equations
[in Russian], Differential'nye Urawneniya, vol. 23, no. 8, 1987, p.p. 1366 - 1376, English transl. in Amer. Math. Society, vol. 23, no. 8,
1988, p.p. 930 - 939.
[4] L. P. Tepoyan, On a Degenerate Differential-Operator Equation of
Higher Order, Izvestya Natsionalnoi Akademii Nauk Armenii.
Matematika, vol. 34, no. 5, p.p. 48 - 56, p.p. 1999.
[5] L. D. Kudryavtzev, On Equivalent Norms in the Weight Spaces, Trudy
Mat. Inst. AN SSSR, vol. 170, p.p. 161 - 190, 1984 [in Russian].
[6] G. H. Hardy, J. E. Littlewood, G.Polya, Inequalities, Cambridge Univ.
Press, Cambridge, 1964.
[7] R. E. Showalter, Hilbert Space Methods for Partial Differential
Equations, Electronic Journal of Differential Equations, Monograph 01,1994.
[8] V. I. Burenkov, Sobolev Spaces on Domains, Teubner, 1999.
[1] A. A. Dezin, Degenerate Operator Equations, Mat. Sbornik, vol. 43, no.
3, pp. 287 - 298, 1982 [in Russian].
[2] A. A. Dezin, Partial Differential Equations (An Introduction to a General
Theory of Linear Boundary Value Problems), Springer, 1987.
[3] L. Tepoyan, Degenerate Fourth-Order Differential-Operator Equations
[in Russian], Differential'nye Urawneniya, vol. 23, no. 8, 1987, p.p. 1366 - 1376, English transl. in Amer. Math. Society, vol. 23, no. 8,
1988, p.p. 930 - 939.
[4] L. P. Tepoyan, On a Degenerate Differential-Operator Equation of
Higher Order, Izvestya Natsionalnoi Akademii Nauk Armenii.
Matematika, vol. 34, no. 5, p.p. 48 - 56, p.p. 1999.
[5] L. D. Kudryavtzev, On Equivalent Norms in the Weight Spaces, Trudy
Mat. Inst. AN SSSR, vol. 170, p.p. 161 - 190, 1984 [in Russian].
[6] G. H. Hardy, J. E. Littlewood, G.Polya, Inequalities, Cambridge Univ.
Press, Cambridge, 1964.
[7] R. E. Showalter, Hilbert Space Methods for Partial Differential
Equations, Electronic Journal of Differential Equations, Monograph 01,1994.
[8] V. I. Burenkov, Sobolev Spaces on Domains, Teubner, 1999.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56577", author = "Marziyeh Halimi and Roushanak Lotfikar and Simin Mansouri Borojeni", title = "Solving of the Fourth Order Differential Equations with the Neumann Problem", abstract = "In this paper we considered the Neumann problem for
the fourth order differential equation. First we define the weighted Sobolev space
2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution,
as well as give the description of the spectrum and of the domain of definition of the corresponding operator.", keywords = "Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators.2000 mathematic subject classification: 34A05, 34A30.", volume = "5", number = "10", pages = "1604-3", }