Malaysian Journal of Mathematical Sciences, July 2009, Vol. 3, No. 2
Solvability and Spectral Properties of Boundary Value Problems for Equations of Even Order
D. j. Amanov and A. V. Yuldasheva
Corresponding Email: amanov_d@rambler.ru
Received date: -
Accepted date: -
Abstract:
We study boundary value problems for an equation of the order $2k$ and prove regular and strong solvability of it, investigate spectrum of the problem. In case of even $k$ we obtain a priori estimate for the solution in the norm of the Sobolev space and prove solvability almost everywhere.
Keywords: solvability, boundary value problem, spectrum, a priori estimate, regular solvability, strong solvability, the Fourier series, the Cauchy-Schwarz inequality, the Bessel inequality, the Perceval equality, the Lipchitz condition, even, odd, almost everywhere solution
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