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

Lucio Boccardo; Gisella Croce

doi:10.4171/pm/2041

JournalspmVol. 76, No. 3/4pp. 407–415

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

Lucio Boccardo
Università di Roma La Sapienza, Italy
Gisella Croce
Université du Havre Normandie, Le Havre, France

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Abstract

In this paper we study the existence and regularity of solutions to the following Dirichlet problem

⎩ ⎨ ⎧ - div (a (x) ∣\nabla u ∣^{p - 2} \nabla u) + u ∣ u ∣^{r - 1} = \frac{f ( x )}{u ^{θ}} u > 0 u = 0 in Ω, in Ω, on \partial Ω

proving that the lower order term $u ∣ u ∣^{r - 1}$ has some regularizing effects on the solutions.

Cite this article

Lucio Boccardo, Gisella Croce, The impact of a lower order term in a Dirichlet problem with a singular nonlinearity. Port. Math. 76 (2019), no. 3/4, pp. 407–415

DOI 10.4171/PM/2041