Bir Homojen Sınır-Değer Probleminin İç Kompaktlığı Üzerine

Yıl 2010, Cilt: 26 Sayı: 3, 283 - 290, 01.06.2010

S. S. Mirzoev L. A. Rustamova

Öz

Makalede ikinci mertebe katsayıları singüler (tekil) olan homojen operator diferansiyel denklemler sınıfı için bir sınır değer probleminde regüler (düzgün) çözümlerin varlığı ve tekliğini garanti eden koşullar bulunmuştur. Denklemin yüksek terimi, spektri belli bir sektörde olan normal operator içermektedir. Daha sonra, ele alınan problemin regüler çözümleri uzayının iç kompakt olduğu kanıtlanmıştır.

Anahtar Kelimeler

Normal operator, discontinuous coefficients, regular solvability, Hilbert space

On an Interior Compactness of One Homogeneous Boundary Value Problem

Öz

In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of the equation contains the normal operator the spectrum of which is contained in the certain sectors. Further, it is proved the theorem of internal compactness of space of regular solutions of the considered problem.

Anahtar Kelimeler

Normal operator, discontinuous coefficients, regular solvability, Hilbert space

Kaynakça

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