Volume 27, 2021
|Number of page(s)||17|
|Published online||30 April 2021|
A singular elliptic equation and a related functional*
Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli” Viale Lincoln 5,
2 Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy.
3 Departament d’Anàlisi Matemàtica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain.
** Corresponding author: firstname.lastname@example.org
Accepted: 1 April 2021
where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
Mathematics Subject Classification: 35B25 / 35B27 / 35J25 / 35J67
Key words: Semilinear equations / singularity at u = 0 / existence / uniqueness
© EDP Sciences, SMAI 2021
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