Local behavior for the solutions of a second order nonlinear differential equation

Article type: Research Article

Authors: Salvatori, M.C. | Vitillaro, E.

Affiliations: Dip. di Matematica Università di Perugia, Via Vanvitelli, 1, 06123 Perugia, Italy E-mail: [email protected]

Note: [] Corresponding author.

Note: [] The authors are supported by M.U.R.S.T.

Abstract: In this paper we study the local behavior near zero for the solutions of a class of second order differential equations which include, as a particular case, the radial version of the partial nonlinear differential equation, involving the m-Laplacian operator, div(|∇u|m−2∇u)+f(|x|,u)=0, x∈Rn\{0}, where n>m>1. Some important examples of f are given by f(t,u)=Ctνu|u|q−2  and  f(u)=C1u|u|p−2+C2u|u|q−2. As an application of our general results to the first case we extend to m>1 and ν>−m some estimates given in the literature for the Laplacian case m=2 or for ν=0.

DOI: 10.3233/ASY-1996-12104

Journal: Asymptotic Analysis, vol. 12, no. 1, pp. 55-76, 1996