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Portugaliae Mathematica


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Volume 76, Issue 3/4, 2019, pp. 407–415
DOI: 10.4171/PM/2041

Published online: 2020-07-15

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

Lucio Boccardo[1] and Gisella Croce[2]

(1) Università di Roma La Sapienza, Italy
(2) Université du Havre Normandie, Le Havre, France

In this paper we study the existence and regularity of solutions to the following Dirichlet problem $$\begin{cases} -\div(a(x)|\nabla u|^{p-2} \nabla u) + u|u|^{r-1} = \dfrac{f(x)}{u^{\theta}} & \mbox{in $\Omega$,} \\ u > 0 & \mbox{in $\Omega$,} \\ u = 0 & \mbox{on $\partial\Omega$} \\ \end{cases}$$ proving that the lower order term $ u|u|^{r-1}$ has some regularizing effects on the solutions.

Keywords: Weak solution, approximating problems, strong maximum principle, Schauder’s fixed point theorem

Boccardo Lucio, Croce Gisella: The impact of a lower order term in a Dirichlet problem with a singular nonlinearity. Port. Math. 76 (2019), 407-415. doi: 10.4171/PM/2041