Please use this identifier to cite or link to this item: 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.
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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