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Elliptic systems involving critical growth in dimension two
Using minimax methods we study the existence and multiplicity of
solutions for a class of semilinear elliptic nonhomogeneous
systems where the potentials can change sign and the
nonlinearities may be unbounded in $x$ and behave like
$\exp(\alpha s^2)$ when $|s|\rightarrow+\infty$. We establish the
existence of two distinct solutions when the perturbations are
suitably small.