The impact of a lower order term in a dirichlet problem with a singular nonlinearity

Lucio Boccardo (1) , Gisella Croce (2)

1 Dipartimento di Mathematica, Università di Roma
2 LMAH - Laboratoire de Mathématiques Appliquées du Havre

In this paper we study the existence and regularity of solutions to the following Dirichlet problem        −div(a(x)|∇u| p−2 ∇u) + u|u| r−1 = f (x) u θ in Ω, u > 0 in Ω, u = 0 on ∂Ω proving that the lower order term u|u| r−1 has some regularizing effects on the solutions. Mathematics Subject Classification (2010). 35J66, 35J75

Mots clés: Weak solution; approximating problems; strong maximum principle; Schauder's fixed point theorem

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Lucio Boccardo, Gisella Croce. The impact of a lower order term in a dirichlet problem with a singular nonlinearity. Portugaliae Mathematica, In press, 76 (3/4), pp. 407-415. ⟨10.4171/pm/2041⟩. ⟨hal-02421838v2⟩