Electron. J. Diff. Eqns., Vol. 1996(1996), No. 09, pp. 1-11.

ON ELLIPTIC EQUATIONS IN $R^N$ WITH CRITICAL EXPONENTS

C.O. Alves, J.V. Goncalves, & O.H. Miyagaki

Abstract:
In this note we use variational arguments -namely Ekeland's Principle and the Mountain Pass Theorem- to study the equation
$$-\Delta u + a(x)u = \lambda u^q + u^{2^*-1}\quad {\rm in\ } R^N\,.$$
The main concern is overcoming compactness difficulties due both to the unboundedness of the domain $R^N$, and the presence of the critical exponent $2^*= 2N/(N-2)$.

Submitted August 7, 1996. Published October 22, 1996.
Math Subject Class.: 35J20, 35K20.
Key Words: Elliptic equations, unbounded domains, critical exponents, variational methods.

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C.O. Alves
Dep. Mat. Univ. Fed. Paraiba, 58109-970 - Campina Grande(PB), Brasil
E-mail coalves@dme.ufpb.br

J.V. Goncalves
Dep. Mat. Univ. Brasilia, 70.910-900 Brasilia(DF), Brasil
E-mail jv@mat.unb.br

O.H. Miyagaki
Dep. Mat. Univ. Fed. Vicosa, 36570-000 Vicosa(MG), Brasil
E-mail olimpio@mail.ufv.br

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