Kevser Koklu
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If the scalar product is defined in H1 by the formula f(x), g(x) ∈ H1, H1 forms a separable Hilbert space. In this study, in space H1, it is investigated that Green`s function (resolvant) of the operator formed by the differential expression.
(-1)n y (2n) +Q(x)y, |
0 ≤ x ≤ ∞ |
And boundary conditions
Y(j) (0)-h jy
(j-I)(0)=0, |
j = 1,3,......,2n-1 |
Where Q(x) is a normal operator that has pure degree spectrum for every x ∈ [0, ∞) ) in H. Assumed that domain of Q(x) is independent from x and resolvent set of Q(x) belongs to (0 < ∈ ≤ π) of Complex plane λ. In addition assumed that the operator function Q(x) satisfies the Titchmars-Levitan complex conditions. h j are arbitrary complex numbers. The obtained result has been applied to an example.
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How to cite this article
Kevser Koklu, 2002. Resolvent of Fourth Order Differential Equation in Half Axis. Journal of Applied Sciences, 2: 422-428.
DOI: 10.3923/jas.2002.422.428
URL: https://scialert.net/abstract/?doi=jas.2002.422.428
DOI: 10.3923/jas.2002.422.428
URL: https://scialert.net/abstract/?doi=jas.2002.422.428