Elliptic systems involving critical growth in dimension two (Q1035046)

Using maximal methods the author studies the existence and multiplicity of solutions for a class of semilinear elliptic nonhomogeneous systems \[ -\Delta u_i + a_i(x)u_i=g_i(x)f_i(u_1,\dots,u_m) + h_i(x),\quad x\in {\mathbb R^2},\;i=1,\dots,m, \] where the potentials can change sign and the nonlinearities may be unbounded in \(x\) and behave like \(\exp(\alpha s^2)\) when \(|s|\to+\infty\). It is established the existence of two distinct solutions when the perturbations are suitably small.