FOUR FOLD EXPANSION IN SOLVING A BOUNDARY VALUE PROBLEM FOR A FOURTH ORDER DIFFERENTIAL EQUATION WITH DOUBLE CHARACTERISTI

Author(s):  E.G. Orudzhev, Dr., Baku State University, Baku, Republic of Azerbaijan, elsharorucov63@mail.ru

L.I. Amirova, candidate of Sciences, associate Professor, Baku State University, Baku, Republic of Azerbaijan , kamhas06@rambler.ru

Issue:  Volume 51, № 2

Rubric:  Mathematics

Annotation:  On the closed interval [0,1] is considered parametric nearly regular order two differential bundle of fourth order with two double purely imaginary characteristic roots under decaying Sturm type boundary conditions, two of which are given at the left end. The existence is proven the sequence of expanding contours in the plane of the spectral parameter on which the resolvent kernel (the Green function) decreases. According to the solution of the problem, the theorem on the four fold decomposition of sufficiently smooth functions are proved on the base estimate of the Green function on the contours, vanishing together with derivatives of order higher than the order of the equation at the ends of the segment.

Keywords:  regular problems, eigenvalues, Green function, decomposition formula

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