Electron. J. Diff. Eqns., Vol. 1999(1999), No. 39, pp. 1-15.
### Existence results for quasilinear elliptic systems in
R^{N}

N. M. Stavrakakis & N. B. Zographopoulos

**Abstract:**

We prove existence results for the quasilinear elliptic system

,

where
and
may reach the
critical Sobolev exponents, and the coefficient functions a, b,
and d may change sign.
For the unperturbed system (a=0, b=0), we establish the existence
and simplicity of a positive principal eigenvalue, under the assumption that
u(x), v(x) are positive, and
.
An addendum was attached on November 4, 2003.
The results concerning the critical Sobolev exponent are false;
other results still hold. See last page of this article.

Submitted July 16, 1999. Published October 4, 1999.

Math Subject Classifications: 35P30, 35J70, 35B45, 35B65.

Key Words: p-Laplacian, nonlinear eigenvalue problems,
homogeneous Sobolev spaces, maximum principle, Palais-Smale Condition.

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N. M. Stavrakakis (e-mail: nikolas@central.ntua.gr)

N. B. Zographopoulos (e-mail: nz@math.ntua.gr)

Department of Mathematics

National Technical University

Zografou Campus

157 80 Athens, Greece

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