Proceedings of the American Mathematical Society

Author(s): Josephus Hulshof; Robertus C. A. M. van der Vorst
Journal: Proc. Amer. Math. Soc. 124 (1996), 2423-2431.
MSC (1991): Primary 35J55; Secondary 34C37
Retrieve article in: PDF
This article is available free of charge

Abstract: We derive the asymptotic behaviour of the ground states of a system of two coupled semilinear Poisson equations with a strongly indefinite variational structure in the critical Sobolev growth case.

1.: Brezis, H. and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477. MR 84h:35059
2.: Carr, J., Applications of centre manifold theory, Appl. Math. Sc. 35, Springer Verlag, 1981. MR 83g:34039
3.: Chow, S.N. and J.K. Hale, Methods of Bifurcation Theorem, Grundl. der math. Wiss 251, Springer Verlag, 1982. MR 84e:58019
4.: Hulshof, J., Similarity solutions of the porous medium equation with sign changes, J. Math. Anal. Appl., 157, 1991, 75-111. MR 92f:35082
5.: Hulshof, J., Similarity solutions of the $k-\epsilon$ model for turbulence, Report W93-11, Leiden University, 1993. (To appear as Similarity solutions of Barenblatt's model for turbulence, SIAM J. Math. Anal.)
6.: Hulshof, J., A local analysis of similarity solutions of the thin film equation, Report W94-22, Leiden University, 1994.
7.: Hulshof, J, E. Mitidieri and R.C.A.M. van der Vorst, Strongly indefinite systems with critical Sobolev exponents, Report W95-15, Leiden University, 1995.
8.: Hulshof, J. and R.C.A.M. van der Vorst, Positive solutions of the equation $\Delta u+u^p=0$ on a bounded domain, course notes, Report W93-06, Leiden University, 1993.
9.: Hulshof, J. and R.C.A.M. van der Vorst, Differential Systems with Strongly Indefinite Variational Structure, J. Funct. Anal., 114, 1993, 32-58. MR 94g:35073
10.: Lieb, E., Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. Math. 118 (1983), 349-374. MR 86j:42010
11.: Lions, P.L., The concentration-compactness principle in the calculus of variations, part 1, Rev. Mat. Iberoam. 1 (1985), 145-201. MR 87c:49007
12.: Mitidieri, E., A Rellich type identity and applications, Comm. PDE 18 (1993), 125-151. MR 94c:26016
13.: Van der Vorst, R.C.A.M., Best constant for the embedding of the space $H^2 \cap H_0^1$ into $L^{2N/(N-4)}$ , Differential and Integral Equations 6 (1992), 259-276. MR 94b:46053
14.: Wang, X.J., Sharp constant in a Sobolev inequality, Nonlinear Anal. 20 (1993), 261-268. MR 94g:35035
15.: Felmer, P. and D. G. de Figueiredo, On super-quadratic elliptic systems, Trans. A. M. S. 343 (1994), 99--116.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35J55, 34C37

Josephus Hulshof
Affiliation: Mathematical Department of the Leiden University, Niels Bohrweg 1 2333 CA Leiden, The Netherlands
Email: hulshof@wi.leidenuniv.nl

Robertus C. A. M. van der Vorst
Affiliation: Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30308-0190
Email: rvander@math.gatech.edu

DOI: 10.1090/S0002-9939-96-03669-6
PII: S 0002-9939(96)03669-6
Keywords: Systems, strongly indefinite variational structure, critical Sobolev growth, ground states, asymptotic behaviour, transformation to $3$- and $4$-dimensional quadratic systems, heteroclinic orbits, critical point analysis.
Received by editor(s): February 16, 1995
Additional Notes: We gratefully acknowledge the support by N.W.O., the Dutch Organisation for Scientific Research, and Enzo Mitidieri for his encouragement.
Communicated by: Jeffrey Rauch
Copyright of article: Copyright 1996, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS