Asymptotic Behavior of Ground States of Quasilinear Elliptic Problems with Two Vanishing Parameters
نویسندگان
چکیده
– We study the asymptotic behavior of the radially symmetric ground state solution of a quasilinear elliptic equation involving the m-Laplacian. The case of two vanishing parameters is considered: we show that these two parameters have opposite effects on the asymptotic behavior. Moreover the results highlight a suprising phenomenon: different asymptotic are obtained according to whether n > m2 or n m2, where n is the dimension of the underlying space. 2002 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Nous étudions le comportement asymptotique de l’état fondamental à symétrie radiale d’une équation elliptique quasilinéaire contenant le m-Laplacien. Le cas de deux paramètres tendant vers 0 est considéré : nous montrons que ces deux paramètres sont en compétition. Les résultats obtenus découvrent un nouveau surprenant phénomène : deux comportements asymptotiques complètement différents sont obtenus suivant une relation entre le paramètre m et la dimension n de l’espace. 2002 Éditions scientifiques et médicales Elsevier SAS
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