On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity

Autor(es)

Pimenta, Marcos T. O. ; dos Santos, Gelson Conceicao G. ; Santos Junior, Joao R.

• Tipo de documento: Artigo Científico
• Fonte: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS; v. N/A, p. 27-pg., 2022-12-28.

Resumo

In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity. (AU)

• Processo FAPESP: 21/10791-1 - Análise não-linear de equações diferenciais parciais elípticas
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil
• Processo FAPESP: 21/04158-4 - Problemas elípticos envolvendo o operador de curvatura-média no espaço das funções de variação limitada
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
• Modalidade de apoio: Auxílio à Pesquisa - Regular