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Separation of the two dimensional Laplace operator by the disconjugacy property | ||
| Iranian Journal of Science | ||
| مقاله 1، دوره 36، شماره 1، اردیبهشت 2012، صفحه 1-6 اصل مقاله (186.21 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2012.2048 | ||
| نویسندگان | ||
| H. A. Atia* 1؛ R. A. Mahmoud2 | ||
| 1Current Address: Mathematics Department, Rabigh College of Science and Art, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia | ||
| 2Zagazig University, Faculty of Science, Mathematics Department, Zagazig, Egypt | ||
| چکیده | ||
| In this paper we have studied the separation for the Laplace differential operator of the form , , in the Hilbert space ², with potential , ¹. We show that certain properties of positive solutions of the disconjugate second order differential expression P[u] imply the separation of minimal and maximal operators determined by P i.e, the property that ² ², ². A property leading to a new proof and generalization of a 1971 separation criterion due to Everitt and Giertz. This result will allow the development of several new sufficient conditions for separation and various inequalities associated with separation. A final result of this paper shows that the disconjugacy of ² for some 0 implies the separation of P. | ||
| کلیدواژهها | ||
| Separation؛ Laplace differential operator؛ Disconjugacy؛ Hilbert space | ||
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