Critical and subcritical elliptic systems in dimension two

By Djairo, D. Figueiredo, DO Joãomarcos, Bernhard Ruf. 2004

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Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, background): “(K4) there exist M > 0 and t1 > 0 such that for all t ≥ t1, one has 0 < F(t) ≤ Mf (t) and 0 < G(t) ≤ Mg(t), then [18] has the following result.”
Elliptic Systems with Nonlinearities of Arbitrary Growth (2004, unknown): “Then, writing u = ∞∑ n=1 anen , with an = ∫ Ω uendx , we set Es = {u ∈ L2(Ω) : ∞∑ n=1 λsn|an|2 ∞} and define a linear operator on L2(Ω) by Asu = ∞∑ n=1 λs/2n anen , ∀ u ∈ D(As) := Es .”
On a quasilinear nonhomogeneous elliptic equation with critical growth in R N (2009, background): “For problems involving critical growth in the Trudinger–Moser case, see [2–4,7,10,11,14–18, 28,29,32,34] and references therein.”