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http://hdl.handle.net/10077/4825
Title: | Nodal regions for solutions of nonlinear elliptic problems | Authors: | Di Piazza, Luisa Maniscalco, Caterina |
Issue Date: | 1990 | Publisher: | Università degli Studi di Trieste. Dipartimento di Scienze Matematiche | Source: | Luisa Di Piazza, Caterina Maniscalco, “Nodal regions for solutions of nonlinear elliptic problems”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 22 (1990), pp. 91-108. | Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics 22 (1990) |
Abstract: | In questo lavoro, mediante la teoria di Morse, viene data una stima del numero delle regioni nodali delle soluzioni del problema $-\Delta u=\lambda c(x)u+\mid u\mid^{p-2}u\: in\:\Omega,\: u\epsilon H_{0}^{1}(\Omega),\: dove\:\Omega\subset\mathbf{R^{\textrm{n}}},N\geq3$, è un aperto connesso, limitato e regolare, $p\epsilon(2,2N/(N-2],$ c(x) $\epsilon L^{q}(\Omega),$ q > p/(p-2) e $\lambda\epsilon\mathbf{R}$. In this paper we are concerned with the problem $-\Delta u=\lambda c(x)u+\mid u\mid^{p-2}u\: in\:\Omega,\: u\epsilon H_{0}^{1}(\Omega),\: where\:\Omega\subset\mathbf{R^{\textrm{n}}},N\geq3$, is a smooth bounded domain, $p\epsilon(2,2N/(N-2],$ c(x) $\epsilon L^{q}(\Omega),$ q > p/(p-2) and $\lambda\epsilon\mathbf{R}$. Using the Morse theory, we estimate the number of the nodal regions of the solutions of the above problem. |
Type: | Article | URI: | http://hdl.handle.net/10077/4825 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.22 (1990) |
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