Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems

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Lane–Emden systems with negative exponents (2010, unknown): “, [1, 3, 6, 7, 16, 18, 19, 20, 21, 22, 23] and the references therein).”
Liouville type theorems for integral equations and integral systems (2013, background): “Whenα = 2, there are a great number of results on the nonexistence results of (3) and (4), see [1,3,4,13–15,28].”
Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ N (2008, methodology): “Recently, by the monotonicity result by Busca and Manásevich (2002), De Figueiredo and Sirakov (2005) proved some Liouville type results for bounded positive solutions for systems: u1 + u 1 1 + u 1 2−1 1−1 2 = 0 u2 + u 2 1−1 2−1 1 + u 22 = 0 (1.7) does not have bounded positive classical solution…”
L∞-Estimates for nonlinear elliptic Neumann boundary value problems (2010, result): “with p;q > 0 and the same assumptions on and . To obtain a priori estimates for elliptic systems of Laplace type we also refer to the publications in [ 11 ] and [28].”