Construction of two-sided approximations to positive solutions of semilinear Navier problem
Keywords:
positive solution, semilinear Navier problem, heterotone operator, two-sided approach
Abstract
A homogeneous Navier problem for a semilinear four-order elliptic equations has been considered. To construct two-way approximations to a positive solution of this problem the methods of the theory of semi-ordered spaces, in particular, the results of V.I. Opoĭcev on the solvability of operator equations with a heterotone operator has been used. The work and the effectiveness of the developed method have been demonstrated by a computational experiment for the problem with power non-linearity.Downloads
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References
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Красносельский М.А. Положительные решения операторных уравнений. – М.: Физматгиз, 1962. – 394 с.
Курпель Н.С., Шувар Б.А. Двусторонние операторные неравенства и их применение. – К.: Наук. думка, 1980. – 268 с.
Опойцев В.И., Хуродзе Т.А. Нелинейные операторы в пространствах с конусом. – Тбилиси: Изд-во Тбилис. ун-та, 1984. – 246 с.
Рвачев В.Л. Теория R-функций и некоторые ее приложения. – К.: Наук. думка, 1982. – 552 с.
Baraket S., Bazarbacha I., Trabelsi N. Construction of singular limits for four-dimensional elliptic problems with exponentially dominated nonlinearity // Bulletin des Sciences Mathematiques. – 2007. – Vol. 131. – №. 7. – Pp. 670-685.
Dalmasso R. Uniqueness theorems for some fourth-order elliptic equations // Proceedings of the American Mathematical Society. – 1995. – Vol. 123. – №. 4. – Pp. 1177-1183.
Dammak M. et al. Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity adding a singular source term given by Dirac masses //Differential and Integral Equations. – 2008. – Vol. 21. – №. 11-12. – Pp. 1019-1036.
Omrane I. B., Dammak M. A Generalized four dimensional Emden-Fowler equation with exponential nonlinearity // Communications in Applied Analysis. – 2009. – Vol. 13. – №. 3. – Pp. 431.
Peletier L. A., Van der Vorst R. Existence and non-existence of positive solutions of non-linear elliptic systems and the biharmonic equation // Differential and Integral Equations. – 1992. – Vol. 5. – №. 4. – Pp. 747-767.
Van der Vorst R. Fourth order elliptic equations with critical growth // Comptes Rendus-Academie des Sciences Paris Serie 1. – 1995. – Vol. 320. – Pp. 295-295.
Published
2017-10-27
How to Cite
Сидоров, М. В. (2017). Construction of two-sided approximations to positive solutions of semilinear Navier problem. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 34, 58-66. Retrieved from https://periodicals.karazin.ua/mia/article/view/9610
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