A Liouville-type theorem for Lane-Emden systems

By J. Busca, R. Manásevich. 2002

117 citations recorded by the source corpus.

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In Applied Mathematics

Citations in the corpus

Hamiltonian elliptic systems: a guide to variational frameworks (2014, background): “a priori bounds for positive solutions are known to hold under (H1) for N4 (see [86, 105]). For N5, there are some partial results which do not cover entirely the case (p;q) satisfying (H1), namely [33, 105], to which we refer for a more complete HAMILTONIAN ELLIPTIC SYSTEMS: A GUIDE TO VARIATIONAL ”
Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems (2005, methodology): “Then problem (21) has no nontrivial classical solutions provided either max{α, β} ≥ N − 2 (Mitidieri [30], Serrin-Zou [36]), or p, q > 1 and min{α, β} > N − 2 2 (Busca-Manasevich [10]).”
Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems (2007, methodology): “[25, 15, 7, 31, 14, 32]).”
Lane–Emden systems with negative exponents (2010, unknown): “, [1, 3, 6, 7, 16, 18, 19, 20, 21, 22, 23] and the references therein).”
Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems (2008, background): “It is easy to see that, if f :]0,+∞[→]0,+∞[ is nondecreasing and concave function on [0, 1], then the assumptions of Theorem 3.”
Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ N (2008, background): “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 2 2 = 0 (1.”