In this paper we consider equations of the form (A(u′)u′)′+δ(r)A(u′)u′+f(r,u)=0 on the real line, where A=A(p) determines the nonlinearity of the equation in the derivative u′, and f is a continuous function containing the nonlinearity in u. Examples are the Bessel equation, the Lane-Emden equation of astrophysics, the Emden-Fowler equation, the Haraux-Weissler equation, and radial versions of divergence-type quasilinear partial differential equations. The results include generalizations of theorems of Fowler, Levin and Nohel, and Artstein and Infante; we also show the detailed asymptotic behavior of solutions as r→∞ when A, δ and f are of asymptotically algebraic type in their arguments.

Asymptotic properties for solutions of strongly nonlinear second order differential equations

PUCCI, Patrizia;
1990

Abstract

In this paper we consider equations of the form (A(u′)u′)′+δ(r)A(u′)u′+f(r,u)=0 on the real line, where A=A(p) determines the nonlinearity of the equation in the derivative u′, and f is a continuous function containing the nonlinearity in u. Examples are the Bessel equation, the Lane-Emden equation of astrophysics, the Emden-Fowler equation, the Haraux-Weissler equation, and radial versions of divergence-type quasilinear partial differential equations. The results include generalizations of theorems of Fowler, Levin and Nohel, and Artstein and Infante; we also show the detailed asymptotic behavior of solutions as r→∞ when A, δ and f are of asymptotically algebraic type in their arguments.
1990
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/117203
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