A quasilinear elliptic equation with absorption term and Hardy potential
Une équation quasilinéaire avec terme d'absorption et potential de hardy
Résumé
Here we study the positive solutions of the equation
where ∆ p u = div(|∇u| p-2 ∇u) and 1 < p < N, q > p -1, µ, θ ∈ R. We give a complete description of the existence and the asymptotic behaviour of the solutions near the singularity 0, or in an exterior domain. We show that the global solutions R N \ {0} are radial and give their expression according to the position of the Hardy coefficient µ with respect to the critical exponent µ 0 = -( N -p p ) p . Our method consists into proving that any nonradial solution can be compared to a radial one, then making exhaustive radial study by phase-plane techniques. Our results are optimal, extending the known results when µ = 0 or p = 2, with new simpler proofs.They make in evidence interesting phenomena of nonuniqueness when θ + p = 0, and of existence of locally constant solutions when moreover p > 2 .
Domaines
Mathématiques [math]
| Origine | Fichiers produits par l'(les) auteur(s) |
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