| Nonlinear partial differential equations |
ter |
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| Teaching Staff in Charge |
| Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro |
| Aims |
| Content |
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The aim of this course is to present some methods for the treatment of nonlinear elliptic problems.I. Preliminaries of Linear Elliptic Equations: Sobolev spaces, Dirichlet's principle, weak solutions, eigenvalues, maximum principle.II. Fixed Point Methods: the operator form of the Dirichlet problem (in $H_{0}^{1}\left( \Omega \right) $); applications of the Banach, Schauder, Krasnoselskii fixed point theorems; application of the Leray-Schauder fixed point theorem.III. Upper and Lower Solutions Method: ordered Banach spaces, normal and regular cones, monotone iterative principles in ordered Banach spaces, upper and lower solutions of the Dirichlet problem. |
| References |
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1. R. Precup, Ecuatii cu derivate partiale, Transilvania Press, Cluj, 1997.
2. D. O'Regan, R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001. 3. H. Brezis, cours DEA, Paris VI, 1991. 4. H. Brezis, Analyse fonctionnelle, Masson, Paris, 1983. |
| Assessment |