Non-existence and uniqueness results for supercritical semilinear elliptic equations - Mathematics > Analysis of PDEsReportar como inadecuado




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Abstract: Non-existence and uniqueness results are proved for several local andnon-local supercritical bifurcation problems involving a semilinear ellipticequation depending on a parameter. The domain is star-shaped but no othersymmetry assumption is required. Uniqueness holds when the bifurcationparameter is in a certain range. Our approach can be seen, in some cases, as anextension of non-existence results for non-trivial solutions. It is based onRellich-Pohozaev type estimates. Semilinear elliptic equations naturally arisein many applications, for instance in astrophysics, hydrodynamics orthermodynamics. We simplify the proof of earlier results by K. Schmitt and R.Schaaf in the so-called local multiplicative case, extend them to the case of anon-local dependence on the bifurcation parameter and to the additive case,both in local and non-local settings.



Autor: Jean Dolbeault CEREMADE, Robert Stanczy

Fuente: https://arxiv.org/







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