Manabu Naito

TL;DR: On etudie les solutions entieres bornees positives de l'equation elliptique semi-lineaire d'ordre 2: Δu+a(x)f(u)=0, xeR n, ou n≥3 and Δ le laplacien a n dimensions as discussed by the authors.

TL;DR: In this article, the authors considered the fourth order nonlinear differential equation with the following conditions: (a) r(t) is continuous and positive for t ≠ 0, and (b) r t is positive and continuous for t = 0.

TL;DR: In this article, the authors considered the differential equation x" + a(t)f(x) = 0, t > 0, under the condition that lim,.x fl'a(s)ds exists and is finite, and necessary and/or sufficient conditions are given for this equation to have solutions which behave asymptotically like nontrivial linear functions cl + c2t.

TL;DR: In this paper, le comportement asymptotique des solutions de l'equation differentielle non lineaire d'ordre 2(p(t)y')'+f(t,y,y')=0 pour laquelle on a les 2 conditions (A 1 ) p:[0, ∞)→(0,∞) est continue and P(t)=∫ 0 t ds/p(s)→∞, t→0;

TL;DR: On considere des equations aux derivees partielles elliptiques semilineaires du type Δ m u=f(|x|,u), x∈R N, N≥3, ou m≥2 est un entier positif et f une fonction continue dans [0, ∞)×(0,∞). On demontre l'existence de solutions entieres positives a symetrie radiale and on donne leur comportement asymptotique.