Existence of exceptional growing-up solutions for a class of non-linear second order ordinary differential equations

Article type: Research Article

Authors: Souplet, Philippe

Affiliations: Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France

Abstract: We establish the existence of nontrivial global solutions for the ordinary differential equation u″+f(u)=g(u′), when f is at most linear and g is superlinear. We then provide a result of global uniqueness in certain classes of power-like functions for general autonomous second order ordinary differential equations. This result allows us to show the exceptional character of the global solutions for a class of equations including u″+u=|u′|p−1u′, for p>1.

DOI: 10.3233/ASY-1995-11204

Journal: Asymptotic Analysis, vol. 11, no. 2, pp. 185-207, 1995