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Existence of entire solutions for some elliptic systems

Published online by Cambridge University Press:  17 April 2009

Ding Yanheng  and
Li Shujie
Ding Yanheng
Affiliation:
Institute of Mathematics Academia Sinica 100080Beijing People'sRepublic of China
Li Shujie
Affiliation:
International Centre for Theoretical Physics Trieste, Italy
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Abstract

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We establish the existence of solutions for the elliptic systems on ℝN: such that u, v ∈ W1, 2(ℝN), where with q(x)→∞ as |x| → ∞ and (x, u, v) being superlinear or sublinear as .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 3 , December 1994 , pp. 501 - 519
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Benci, V. and Rabinowitz, P.H., ‘Critical point throrems for indefinite functional’, Invent. Math. 52 (1979), 241–273.CrossRefGoogle Scholar
[2]Clément, Ph., de Figueiredo, D.G. and Mitidieri, E., ‘Positive solutions of semilinear elliptic systems’, (preprint).Google Scholar
[3]Ding, Y.H., ‘Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems’, Nonlinear Anal, (to appear).Google Scholar
[4]de Figueiredo, D.G. and Felmer, P.L., ‘On superquadratic elliptic systems’, (preprint).Google Scholar
[5]Kato, T., Perturbation theory for linear operators (Springer-Verlag, Berlin, Heidelberg, New York, 1966).Google Scholar
[6]Krasnoselski, M.A., Topological methods in the theory of nonlinear integral equations (Macmillan, New York, 1964).Google Scholar
[7]Reed, M. and Simon, B., Methods of modern mathematical physics: IV, Analysis of Operators (Academic Press, 1978).Google Scholar
[8]Szulkin, A., ‘Bifurcation for strongly indefinite functionals and Liapunov type theorem for Hamiltonian systems’, Differential Integral Equations 7 (1994), 217–234.CrossRefGoogle Scholar