Pimenta, Marcos T. O.; dos Santos, Gelson Conceição G.; Santos Júnior, João R. On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity. (English) Zbl 07796357 Proc. R. Soc. Edinb., Sect. A, Math. 154, No. 1, 33-59 (2024). MSC: 35J92 35A01 35B40 PDFBibTeX XMLCite \textit{M. T. O. Pimenta} et al., Proc. R. Soc. Edinb., Sect. A, Math. 154, No. 1, 33--59 (2024; Zbl 07796357) Full Text: DOI arXiv
Pimenta, Marcos T. O.; dos Santos Gonzaga, Anderson Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator. (English) Zbl 1520.35075 Commun. Contemp. Math. 25, No. 8, Article ID 2250021, 21 p. (2023). MSC: 35J62 35A01 PDFBibTeX XMLCite \textit{M. T. O. Pimenta} and \textit{A. dos Santos Gonzaga}, Commun. Contemp. Math. 25, No. 8, Article ID 2250021, 21 p. (2023; Zbl 1520.35075) Full Text: DOI
Chata, Juan Carlos Ortiz; Pimenta, Marcos T. O.; de León, Sergio Segura Existence of solutions to a 1-Laplacian problem with a concave-convex nonlinearity. (English) Zbl 1514.35233 J. Math. Anal. Appl. 525, No. 2, Article ID 127149, 25 p. (2023). MSC: 35J92 35A01 PDFBibTeX XMLCite \textit{J. C. O. Chata} et al., J. Math. Anal. Appl. 525, No. 2, Article ID 127149, 25 p. (2023; Zbl 1514.35233) Full Text: DOI
Figueiredo, Giovany M.; Pimenta, Marcos T. O. Nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator via variational and approximation methods. (English) Zbl 1490.35165 Indiana Univ. Math. J. 71, No. 2, 439-462 (2022). MSC: 35J62 35A01 35A15 PDFBibTeX XMLCite \textit{G. M. Figueiredo} and \textit{M. T. O. Pimenta}, Indiana Univ. Math. J. 71, No. 2, 439--462 (2022; Zbl 1490.35165) Full Text: DOI
dos Santos, Gelson; Figueiredo, Giovany M.; Pimenta, Marcos T. O. Multiple ordered solutions for a class of problems involving the 1-Laplacian operator. (English) Zbl 1485.35246 J. Geom. Anal. 32, No. 4, Paper No. 140, 13 p. (2022). MSC: 35J92 35J25 35A01 PDFBibTeX XMLCite \textit{G. dos Santos} et al., J. Geom. Anal. 32, No. 4, Paper No. 140, 13 p. (2022; Zbl 1485.35246) Full Text: DOI
Alves, Claudianor O.; Ourraoui, Anass; Pimenta, Marcos T. O. Multiplicity of solutions for a class of quasilinear problems involving the \(1\)-Laplacian operator with critical growth. (English) Zbl 1480.35202 J. Differ. Equations 308, 545-574 (2022). MSC: 35J62 35A01 35J20 PDFBibTeX XMLCite \textit{C. O. Alves} et al., J. Differ. Equations 308, 545--574 (2022; Zbl 1480.35202) Full Text: DOI arXiv
Ortiz Chata, Juan C.; Pimenta, Marcos T. O.; Segura de León, Sergio Anisotropic 1-Laplacian problems with unbounded weights. (English) Zbl 1479.35489 NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 6, Paper No. 57, 40 p. (2021). MSC: 35J92 35A01 35A15 PDFBibTeX XMLCite \textit{J. C. Ortiz Chata} et al., NoDEA, Nonlinear Differ. Equ. Appl. 28, No. 6, Paper No. 57, 40 p. (2021; Zbl 1479.35489) Full Text: DOI
Ortiz Chata, Juan C.; Pimenta, Marcos T. O. A Berestycki-Lions’ type result to a quasilinear elliptic problem involving the 1-Laplacian operator. (English) Zbl 1464.35141 J. Math. Anal. Appl. 500, No. 1, Article ID 125074, 21 p. (2021). MSC: 35J92 35A01 PDFBibTeX XMLCite \textit{J. C. Ortiz Chata} and \textit{M. T. O. Pimenta}, J. Math. Anal. Appl. 500, No. 1, Article ID 125074, 21 p. (2021; Zbl 1464.35141) Full Text: DOI
Hurtado, Elard Juárez; Pimenta, Marcos T. O.; Miyagaki, Olimpio Hiroshi On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result. (English) Zbl 1460.35169 ESAIM, Control Optim. Calc. Var. 26, Paper No. 86, 20 p. (2020). MSC: 35J91 35J30 35J62 35B65 35J35 PDFBibTeX XMLCite \textit{E. J. Hurtado} et al., ESAIM, Control Optim. Calc. Var. 26, Paper No. 86, 20 p. (2020; Zbl 1460.35169) Full Text: DOI
Alves, Claudianor O.; Figueiredo, Giovany M.; Pimenta, Marcos T. O. Existence and profile of ground-state solutions to a 1-Laplacian problem in \(\mathbb{R}^N\). (English) Zbl 1448.35253 Bull. Braz. Math. Soc. (N.S.) 51, No. 3, 863-886 (2020). MSC: 35J92 35A01 35J20 PDFBibTeX XMLCite \textit{C. O. Alves} et al., Bull. Braz. Math. Soc. (N.S.) 51, No. 3, 863--886 (2020; Zbl 1448.35253) Full Text: DOI arXiv
Figueiredo, Giovany M.; Pimenta, Marcos T. O. Sub-supersolution method for a quasilinear elliptic problem involving the 1-Laplacian operator and a gradient term. (English) Zbl 1435.35171 J. Funct. Anal. 278, No. 3, Article ID 108325, 25 p. (2020). Reviewer: Georgios Psaradakis (Mannheim) MSC: 35J62 35J75 PDFBibTeX XMLCite \textit{G. M. Figueiredo} and \textit{M. T. O. Pimenta}, J. Funct. Anal. 278, No. 3, Article ID 108325, 25 p. (2020; Zbl 1435.35171) Full Text: DOI
Figueiredo, Giovany M.; Pimenta, Marcos T. O. Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions. (English) Zbl 1419.35050 NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 5, Paper No. 47, 18 p. (2018). MSC: 35J62 35J93 PDFBibTeX XMLCite \textit{G. M. Figueiredo} and \textit{M. T. O. Pimenta}, NoDEA, Nonlinear Differ. Equ. Appl. 25, No. 5, Paper No. 47, 18 p. (2018; Zbl 1419.35050) Full Text: DOI arXiv Link
Figueiredo, Giovany M.; Pimenta, Marcos T. O.; Siciliano, Gaetano Multiplicity results for the fractional Laplacian in expanding domains. (English) Zbl 1393.35272 Mediterr. J. Math. 15, No. 3, Paper No. 137, 23 p. (2018). MSC: 35R11 35A15 35S05 58E05 PDFBibTeX XMLCite \textit{G. M. Figueiredo} et al., Mediterr. J. Math. 15, No. 3, Paper No. 137, 23 p. (2018; Zbl 1393.35272) Full Text: DOI arXiv Link
Figueiredo, Giovany M.; Pimenta, Marcos T. O. Strauss’ and Lions’ type results in \(BV(\mathbb R^N)\) with an application to an 1-Laplacian problem. (English) Zbl 1394.35205 Milan J. Math. 86, No. 1, 15-30 (2018). MSC: 35J92 PDFBibTeX XMLCite \textit{G. M. Figueiredo} and \textit{M. T. O. Pimenta}, Milan J. Math. 86, No. 1, 15--30 (2018; Zbl 1394.35205) Full Text: DOI arXiv
Barile, Sara; Pimenta, Marcos T. O. Some existence results of bounded variation solutions to 1-biharmonic problems. (English) Zbl 1392.35149 J. Math. Anal. Appl. 463, No. 2, 726-743 (2018). MSC: 35J62 31B30 PDFBibTeX XMLCite \textit{S. Barile} and \textit{M. T. O. Pimenta}, J. Math. Anal. Appl. 463, No. 2, 726--743 (2018; Zbl 1392.35149) Full Text: DOI
Figueiredo, Giovany M.; Pimenta, Marcos T. O. Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials. (English) Zbl 1382.35114 J. Math. Anal. Appl. 459, No. 2, 861-878 (2018). MSC: 35J92 PDFBibTeX XMLCite \textit{G. M. Figueiredo} and \textit{M. T. O. Pimenta}, J. Math. Anal. Appl. 459, No. 2, 861--878 (2018; Zbl 1382.35114) Full Text: DOI arXiv
Alves, Claudianor O.; Pimenta, Marcos T. O. On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator. (English) Zbl 1380.35103 Calc. Var. Partial Differ. Equ. 56, No. 5, Paper No. 143, 24 p. (2017). Reviewer: Giuseppe Buttazzo (Pisa) MSC: 35J62 35J20 PDFBibTeX XMLCite \textit{C. O. Alves} and \textit{M. T. O. Pimenta}, Calc. Var. Partial Differ. Equ. 56, No. 5, Paper No. 143, 24 p. (2017; Zbl 1380.35103) Full Text: DOI arXiv Link
Figueiredo, Giovany M.; Pimenta, Marcos T. O. Existence of ground state solutions to Dirac equations with vanishing potentials at infinity. (English) Zbl 1352.35141 J. Differ. Equations 262, No. 1, 486-505 (2017). MSC: 35Q41 35A15 35A01 PDFBibTeX XMLCite \textit{G. M. Figueiredo} and \textit{M. T. O. Pimenta}, J. Differ. Equations 262, No. 1, 486--505 (2017; Zbl 1352.35141) Full Text: DOI arXiv
Pimenta, Marcos T. O. Radial sign-changing solutions to biharmonic nonlinear Schrödinger equations. (English) Zbl 1311.35101 Bound. Value Probl. 2015, Paper No. 21, 17 p. (2015). MSC: 35J35 35J60 35Q55 PDFBibTeX XMLCite \textit{M. T. O. Pimenta}, Bound. Value Probl. 2015, Paper No. 21, 17 p. (2015; Zbl 1311.35101) Full Text: DOI arXiv
Pimenta, Marcos T. O.; Soares, Sérgio H. M. Existence and concentration of solutions for a class of biharmonic equations. (English) Zbl 1237.31005 J. Math. Anal. Appl. 390, No. 1, 274-289 (2012). Reviewer: Marius Ghergu (Dublin) MSC: 31B30 35G20 PDFBibTeX XMLCite \textit{M. T. O. Pimenta} and \textit{S. H. M. Soares}, J. Math. Anal. Appl. 390, No. 1, 274--289 (2012; Zbl 1237.31005) Full Text: DOI arXiv