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Mathematical Modelling

Sturm–Liouville abstract problems for the second order differential equations in a non commutative case

M. Kaid, Kh. Ould Melha

Université Abdelhamid Ibn Badis, Mostaganem, Algérie

Abstract: In this paper we prove some new results on Sturm–Liouville abstract problems of the second order differential equations of elliptic type in a new non-commutative framework. We study the case when the second member belongs to a Sobolov space. Existence, uniqueness and optimal regularity of the strict solution are proved. This paper is naturally the continuation of the ones studied by Cheggag et al in the commutative case. We also give an example to which our theory applies.

Keywords: second-order abstract elliptic differential equations; Sturm–Liouville boundary conditions in non commutative cases; analytic semigroup; maximal regularity.

UDC: 517.9

MSC: 35J20, 35J40

Received: 03.06.2018

Language: English

DOI: 10.14529/mmp180304

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