Asymptotic behaviour of ground states

Hulshof, Josephus; van der Vorst, Robertus

doi:10.1090/S0002-9939-96-03669-6

Asymptotic behaviour of ground states
HTML articles powered by AMS MathViewer

by Josephus Hulshof and Robertus C. A. M. van der Vorst PDF

Proc. Amer. Math. Soc. 124 (1996), 2423-2431 Request permission

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.

References

Haïm Brézis and Louis Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437–477. MR 709644, DOI 10.1002/cpa.3160360405
Jack Carr, Applications of centre manifold theory, Applied Mathematical Sciences, vol. 35, Springer-Verlag, New York-Berlin, 1981. MR 635782, DOI 10.1007/978-1-4612-5929-9
Shui Nee Chow and Jack K. Hale, Methods of bifurcation theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 251, Springer-Verlag, New York-Berlin, 1982. MR 660633, DOI 10.1007/978-1-4613-8159-4
Josephus Hulshof, Similarity solutions of the porous medium equation with sign changes, J. Math. Anal. Appl. 157 (1991), no. 1, 75–111. MR 1109445, DOI 10.1016/0022-247X(91)90138-P
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.)
Hulshof, J., A local analysis of similarity solutions of the thin film equation, Report W94-22, Leiden University, 1994.
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.
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.
Josephus Hulshof and Robertus van der Vorst, Differential systems with strongly indefinite variational structure, J. Funct. Anal. 114 (1993), no. 1, 32–58. MR 1220982, DOI 10.1006/jfan.1993.1062
Huzoor H. Khan, A note on a theorem of Izumi, Comm. Fac. Sci. Univ. Ankara Sér. $A_1$ Math. 31 (1982), no. 14, 123–127 (1984). MR 794035
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. I, Rev. Mat. Iberoamericana 1 (1985), no. 1, 145–201. MR 834360, DOI 10.4171/RMI/6
Enzo Mitidieri, A Rellich type identity and applications, Comm. Partial Differential Equations 18 (1993), no. 1-2, 125–151. MR 1211727, DOI 10.1080/03605309308820923
R. C. A. M. Van der Vorst, Best constant for the embedding of the space $H^2\cap H^1_0(\Omega )$ into $L^{2N/(N-4)}(\Omega )$, Differential Integral Equations 6 (1993), no. 2, 259–276. MR 1195382
Xu Jia Wang, Sharp constant in a Sobolev inequality, Nonlinear Anal. 20 (1993), no. 3, 261–268. MR 1202203, DOI 10.1016/0362-546X(93)90162-L
Felmer, P. and D. G. de Figueiredo, On super-quadratic elliptic systems, Trans. A. M. S. 343 (1994), 99–116.