Manabu Naito

Oscillation theorems for semilinear elliptic differential operators

The semilinear elliptic differential operator L [ u ] = Δ u + c ( x, u ) is studied and sufficient conditions are derived for all solutions of uL [ u ] ≦ 0 with suitable boundary conditions to be oscillatory in unbounded domains of R n . Here, unbounded domains to be considered are cones, strips and cylinders in R n . The results are based on the conditions for the non-existence of positive solutions of ordinary differential inequalities.

Entire Solutions of a Class of Even Order Quasilinear Elliptic Equations

On demontre lexistence de solutions entieres radialement symetriques et on decrit leur comportement asymptotique pour |x|→∞

Positive solutions of a class of nonlinear ordinary differential equations

On considere lequation differentielle non lineaire: x (n) +σf(t,x)=o, t≥t 0 , ou n≥2, T=+1 ou T=−1, et f:[t 0 ,∞)×(o,∞)→R est une fonction continue telle que f(t,x)≥o pour tout (t,x)∈[t 0 ,∞)×(o,∞)

On the Elliptic Equation Δu = φ(x) u γ in R 2

On considere le cas γ¬=1 et O(x)≥0 est localement continue de Holder. On obtient des conditions suffisantes pour que cette equation possede un nombre infini de solutions positives definies sur R 2 et ayant une croissance logarithmique quand |x|→∞