Local behaviour of the solutions of a class of nonlinear elliptic systems

By Marie-Franccoise Bidaut-V'eron. Advances in Differential Equations, 2000

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Here we study the behaviour near a punctual singularity of the positive solutions of semilinear elliptic systems in R (N 3) given by u+ jxj uv = 0; v + jxj uv = 0; (where a; b; p; q; s; t 2 R , p; q > 0; s; t 0 ). We describe the rst undercritical case, and the sublinear and linear cases. The proofs do not use any variational methods, but lie essentially upon comparison properties between the two solutions u and v, and the properties of the subsolutions and supersolutions of the scalar equation f + jxj f = 0 ( ; 2 R , > 0). This extends the classical study of the scalar equation when 0 < < max (N; (N + ))=(N 2).

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b164a9fac45c52d8ec7102ae8b3f422fa4fc099

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In Applied Mathematics

In Computational Theory and Mathematics

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Citations in the corpus

Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle (2010, result): “ the operator F (as found in [2]). As far as systems of inequalities are concerned, Liouville results were obtained by Mitidieri [34], Serrin and Zou [39], for the case of a whole space, Bidaut-Veron [8] for quasilinear systems in exterior domains, Birindelli and Mitidieri [10], Laptev [29] for syst”
Singularity and decay estimates in superlinear problems via Liouville-type theorems, I: Elliptic equations and systems (2007, background): “range max(α, β) < n − 2, a classification of singularities has been obtained in [3].”