Nonexistence results for a class of nonlinear elliptic equations involving critical Sobolev exponents

Cristina Tarsi

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Nonexistence results for a class of nonlinear elliptic equations involving critical Sobolev exponents

Cristina Tarsi

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Abstract

In this paper we study the problem of bifurcation from the origin of solutions of elliptic Dirichlet problems involving critical Sobolev exponent, defined on a bounded domain $Ω$ in $\mathbb{R} ^N$: we prove that the first critical case are $N=3, 4$ (not only N=3, as just proved by Brezis and Nirenberg), exhibiting two nonexistence results for a class of elliptic problem in these dimensions.

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Cristina Tarsi. 2004-11-12. Nonexistence results for a class of nonlinear elliptic equations involving critical Sobolev exponents. https://arxiv.org/abs/math/0411285

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