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Article Contents

# 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.
Mathematics Subject Classification: Primary: 35J50, 35J55; Secondary: 35Q55.

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