Abstract
We investigate the existence of positive solutions of a Dirich let problem for the system \( - \Updelta u = f(v),\,\Updelta v = g(u) \) in a bounded convex domain Ω of \( {\mathbb{R}}^{N} \) with smooth boundary. In particular L ∞ a priori bounds are obtained in the same spirit as in De Figueiredo—Lions—Nussbaum [7].
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Added In Proof
The assumption (f1) can be relaxed if one assumes that Ω is a ball. This was done recently in: L. A. Peletier and R.C. A.M. van der Vorst, Existence and Non-Existence of Positive Solutions of Non-Linear Elliptic Systems and the Bi-Harmonic Equation, to appear in Diff. and Int. Eq.
Acknowledgments
The authors would like to thank the referee for several helpful comments. The work of E. Mitidieri was supported by C.N.R. (Fondi 60 %).
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© 1992 Marcel Dekker, Inc.
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Clkment, P., de Figueiredo, D.G., Mitidieri, E. (1992). Positive Solutions of Semilinear Elliptic Systems. In: Costa, D. (eds) Djairo G. de Figueiredo - Selected Papers. Springer, Cham. https://doi.org/10.1007/978-3-319-02856-9_25
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DOI: https://doi.org/10.1007/978-3-319-02856-9_25
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