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Asymptotics for Semilinear Elliptic Systems

Published online by Cambridge University Press:  20 November 2018

Ezzat S. Noussair  and
Charles A. Swanson
Ezzat S. Noussair
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W., Australia 2033
Charles A. Swanson
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Y4
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Abstract

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A class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in ℝN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N) as |x| —> ∞. Additional results concern the existence and structure of positive solutions u with finite energy in a neighbourhood of infinity.

Keywords

35J6035B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 514 - 519
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Brezis, H. and Kato, T., Remarks on the Schrodinger operator with singular complex potential, J. Math Pures App. 58 (1979), 137–151.Google Scholar
2. Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order. 2nd éd., Springer- Verlag, Berlin-Heidelberg-New York-Tokyo, 1983.Google Scholar
3. Kawano, N., On bounded entire solutions of semilinear elliptic equations, Hiroshima Math. J. 14 (1984), 125–158.Google Scholar
4. Kawano, N. and Kusano, T., On positive entire solutions of a class of second order semilinear elliptic systems, Math. Z. 186 (1984), 287–297.Google Scholar
5. Miranda, C., Partial differential equations of elliptic type. Springer- Verlag, New York-Heidelberg-Berlin, 1970.Google Scholar
6. Noussair, E. S. and Swanson, C. A., Oscillation theory for semilinear Schrodingerequations and inequalities, Proc. Roy. Soc. Edinburgh A75( 1975/76), 67–81.Google Scholar
7. Noussair, E. S. and Swanson, C. A., Global positive solutions of semilinear elliptic equations, Canad. J. Math. 35 (1983), 839–861.Google Scholar
8. Serrin, J., Isolated singularities of solutions of quasi-linear equations, Acta Math. 113 (1965), 219–240.Google Scholar
9. Swanson, C. A., Extremal positive solutions of semilinear Schrodinger equations, Canad. Math Bull. 26 (1983), 171-178.Google Scholar
10. Swanson, C. A., Positive solutions of -Δu =f(x,u), Nonlinear Anal. 9 (1985), 1319–1323.Google Scholar