The Liouville theorem for a quasi-linear elliptic partial differential equation
| Autor: | S. Elwood Bohn, Lloyd K. Jackson |
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| Rok vydání: | 1962 |
| Předmět: |
Pure mathematics
Partial differential equation Elliptic partial differential equation Real-valued function Applied Mathematics General Mathematics Bounded function Mathematical analysis First-order partial differential equation Elliptic function Hyperbolic partial differential equation Parabolic partial differential equation Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 104:392-397 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/s0002-9947-1962-0139840-6 |
| Popis: | If z(x, y) is a real valued function of the real variables x and y which is a solution of Zxx+z = 0 and is bounded either above or below throughout the finite plane, then z(x, y) is a constant. Here we are concerned with the question of whether or not the second formulation of the above theorem is valid for solutions of more general elliptic partial differential equations. In what follows the usual notation will be |
| Databáze: | OpenAIRE |
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