On the existence of radial solutions of quasilinear elliptic equations

Satyanad Kichenassamy (1) , Joel Smoller

1 CIMS - Courant Institute of Mathematical Sciences [New York]

We give a method for proving the existence of (positive) radial solutions of quasi-linear elliptic equations, taking into account the variation of lower-order terms. We find solutions of equations having oscillating nonlinearities, under less restrictive conditions than those needed for variational or topological methods. We exhibit simple variational problems having a continuum of solutions. We also obtain invariant regions in $C^1$, for related parabolic problems.

Domaines: Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Satyanad Kichenassamy, Joel Smoller. On the existence of radial solutions of quasilinear elliptic equations. Nonlinearity, 1990, 3, pp.677-694. ⟨10.1088/0951-7715/3/3/008⟩. ⟨hal-00002659⟩