On nonhomogeneous elliptic equations involving critical Sobolev exponent
G. Tarantello
Carnegie Mellon University, Department of Mathematics, Pittsburgh, PA 15213, U.S.A
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Abstract
Let , be the limiting Sobolev exponent and open bounded set.
We show that for satisfying a suitable condition and , the Dirichlet problem:
admits two solutions and in .
Also and for .
Notice that, in general, this is not the case if (see [P]).
Résumé
Soit l’exposant de Sobolev critique et un domaine borné.
On montre que si , satisfait une certaine condition alors le problème de Dirichlet : dans et dans , admet deux solutions et dans . De plus et si .
On remarque que ce n’est pas le cas, en général, si (voir [P]).
Cite this article
G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), no. 3, pp. 281–304
DOI 10.1016/S0294-1449(16)30238-4