EXISTENCE AND UNIQUENESS OF THE STRONG SOLUTION FOR AN NON-LOCAL BOUNDARY VALUE PROBLEM

Authors

  • A GUEZANE LAKOUD Université de Annaba
  • F REBBANI Université de Annaba

Keywords:

Operator differential equation, Non-local boundary conditions, Energy inequality

Abstract

In this work we are interested in a certain class of equations with operator coefficients and non-local boundary conditions. For the boundary value problem generated by these equations we establish the existence and uniqueness of the strong solution as well as its continuous dependence on the data. We use the method of energy inequality.

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Author Biographies

A GUEZANE LAKOUD, Université de Annaba

Département de Mathématiques
Faculté des sciences

F REBBANI, Université de Annaba

Département de Mathématiques
Faculté des sciences

References

- N. Brich N.I., Yurchuk N.I., "Goursat problem for a second order abstract linear differential equation''. Differ. Uravn., T.7, N° 6, (1971), pp. 1017-1030 (Russian).

- Guezane-Lakoud A., Rebbani F., Yurchuk N.I., ''Problème aux limites pour une équation différentielle opérationnelle de second ordre'', Maghreb. Mathematical Review, Vol.6, N°1, (1997), pp. 39-48 (French).

- Guezane-Lakoud A., Rebbani F., "A priori estimate for hyperbolic abstract equation with non local boundary conditions", Mathematical Maghreb Review, Vol.8, N°1&2, (1999), pp.111-118.

- Guezane-Lakoud A., Rebbani F., "Strong solution for an abstract non local boundary value problem", Int. J. of Applied Math., Vol. 4, N°4, (2000), pp. 469-478.

- Guezane-Lakoud A., "On a class of hyperbolic equation with abstract non-local boundary conditions", Int. J. of Applied Sc. Computations, Vol.8, N°1, (2001).

- Chesalyn V.I., Yurchuk N.I., ''Problem with non-local bundary conditions for an Liav's abstract equation'', I. zv. Akad. Nauk. BSSR. Serie Phys. Mat., N° 6, (1973), pp. 30-35, (Russian).

- Engelman U., "Boundary value problem for an operator hyperbolic partial differential equation of second order with non-local boundary conditions'', Differ. Uravn., T.11, N°9, (1975), pp. 1687-1963 (Russian).

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Published

2002-06-01

How to Cite

GUEZANE LAKOUD, A., & REBBANI, F. (2002). EXISTENCE AND UNIQUENESS OF THE STRONG SOLUTION FOR AN NON-LOCAL BOUNDARY VALUE PROBLEM. Sciences & Technology. A, Exactes Sciences, (17), 11–14. Retrieved from https://revue.umc.edu.dz/a/article/view/1778

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