Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition

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Sharp subcritical Moser-Trudinger inequalities on Heisenberg groups and subelliptic PDEs (2014, unknown): “Moreover, our restriction on the norm ∥∇Hu∥LQ (H) ≤ 1 of the function u is much weaker than ∥∇Hu∥LQ (H) + ∥u∥ LQ (H) ≤ 1 which was assumed in Lam and Lu (2012) [16].”
EXISTENCE OF NONTRIVIAL SOLUTIONS TO POLYHARMONIC EQUATIONS WITH SUBCRITICAL AND CRITICAL EXPONENTIAL GROWTH (2012, methodology): “When m = 1, n = 2, problem (1) becomes the well-known Laplacian problem on bounded domains Ω ⊂ R 2 and has been investigated in [2] [13] [17] [23] [36].”
Trudinger–Moser Inequalities in Fractional Sobolev–Slobodeckij Spaces and Multiplicity of Weak Solutions to the Fractional-Laplacian Equation (2018, methodology): “In [32, 33], Lam and Lu used aweaker condition to replace the Ambrosetti–Rabinowitz condition and got existence results for N-Laplacian and polyharmonic operators without the (AR) condition.”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, unknown): “Existence of solutions to polyharmonic operators and N -Laplacian equations of exponential growth without satisfying the standard Ambrosetti–Rabinowitz condition have been studied by the authors in [41,44,45].”