LOCAL BEHAVIOR AND GLOBAL EXISTENCE OF POSITIVE SOLUTIONS OF au − u u COMPORTEMENT LOCAL ET EXISTENCE GLOBALE DES SOLUTIONS POSITIVES DE au − u u
نویسنده
چکیده
– We study the behavior near the origin of C2 positive solutions u(x) of au − u u (∗) in a punctured neighborhood of the origin in R (n > 2) where the constants λ and a satisfy n n−2 < λ< n+2 n−2 and 0 < a < 1. We also study the existence of C 2 positive solutions of (∗) in R. In both cases we show that changing a from one value in the open interval (0,1) to another value in (0,1) can have a dramatic effect. 2002 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – On étudie le comportement prés de l’ origine des solutions positives de classe C2 u(x) de au − u u (∗) dans un voisinage épointé de l’ origine dans R (n > 2) où les constantes λ et a satisfont n n−2 < λ < n+2 n−2 et 0 < a < 1. On étudie aussi l’ existence de solutions positives de classe C 2 de (∗) dans R. Dans les deux cas nous montrons que changer la valeur de a dans l’intervalle ouvert (0,1) peut avoir un effet dramatique. 2002 Éditions scientifiques et médicales Elsevier SAS
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