Elliptic Neumann problems with highly discontinuous nonlinearities
This paper investigates nonlinear differential problems involving the p-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the e...
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| Published in | Applied mathematics letters Vol. 163; p. 109455 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.04.2025
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| Subjects | |
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| ISSN | 0893-9659 |
| DOI | 10.1016/j.aml.2025.109455 |
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| Abstract | This paper investigates nonlinear differential problems involving the p-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the existence of at least two nontrivial weak solutions of such problems. |
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| AbstractList | This paper investigates nonlinear differential problems involving the p-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the existence of at least two nontrivial weak solutions of such problems. |
| ArticleNumber | 109455 |
| Author | D’Aguì, Giuseppina Winkert, Patrick Morabito, Valeria |
| Author_xml | – sequence: 1 givenname: Giuseppina orcidid: 0000-0003-2080-8181 surname: D’Aguì fullname: D’Aguì, Giuseppina email: dagui@unime.it organization: Department of Engineering, University of Messina, 98166 Messina, Italy – sequence: 2 givenname: Valeria orcidid: 0009-0005-4156-8510 surname: Morabito fullname: Morabito, Valeria email: valeria.morabito2@studenti.unime.it organization: Department of Engineering, University of Messina, 98166 Messina, Italy – sequence: 3 givenname: Patrick orcidid: 0000-0003-0320-7026 surname: Winkert fullname: Winkert, Patrick email: winkert@math.tu-berlin.de organization: Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany |
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| Cites_doi | 10.1016/j.jde.2008.02.025 10.1006/jdeq.2001.4092 10.1016/S0377-0427(99)00269-1 10.1016/0022-247X(81)90095-0 10.1016/S0362-546X(00)00171-1 10.1007/s000130050496 10.1016/s0294-1449(16)30389-4 10.1016/j.na.2011.12.003 |
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| Keywords | Multiple solution Neumann problem 34B15 Discontinuous nonlinearity Nonsmooth analysis 34A36 49J52 35B30 |
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| References | Ricceri (b8) 2000; 75 Bonanno, D’Aguì, Winkert (b11) 2019; 4 Motreanu, Panagiotopoulos (b1) 1999 Bonanno, Candito (b10) 2008; 244 De Giorgi, Buttazzo, Dal Maso (b14) 1983; 74 Marano, Motreanu (b6) 2002; 48 Papageorgiou, Winkert (b13) 2024 Bonanno (b9) 2012; 75 Motreanu, Rădulescu (b12) 2003 Chang (b2) 1981; 80 Marano, Motreanu (b5) 2002; 182 Ricceri (b7) 2000; 113 Szulkin (b4) 1986; 3 Clarke (b3) 1990 Motreanu (10.1016/j.aml.2025.109455_b12) 2003 Bonanno (10.1016/j.aml.2025.109455_b10) 2008; 244 Szulkin (10.1016/j.aml.2025.109455_b4) 1986; 3 Marano (10.1016/j.aml.2025.109455_b5) 2002; 182 Bonanno (10.1016/j.aml.2025.109455_b11) 2019; 4 De Giorgi (10.1016/j.aml.2025.109455_b14) 1983; 74 Chang (10.1016/j.aml.2025.109455_b2) 1981; 80 Ricceri (10.1016/j.aml.2025.109455_b7) 2000; 113 Bonanno (10.1016/j.aml.2025.109455_b9) 2012; 75 Clarke (10.1016/j.aml.2025.109455_b3) 1990 Ricceri (10.1016/j.aml.2025.109455_b8) 2000; 75 Marano (10.1016/j.aml.2025.109455_b6) 2002; 48 Motreanu (10.1016/j.aml.2025.109455_b1) 1999 Papageorgiou (10.1016/j.aml.2025.109455_b13) 2024 |
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Non Linéaire doi: 10.1016/s0294-1449(16)30389-4 – volume: 75 start-page: 2992 issue: 5 year: 2012 ident: 10.1016/j.aml.2025.109455_b9 article-title: A critical point theorem via the Ekeland variational principle publication-title: Nonlinear Anal. doi: 10.1016/j.na.2011.12.003 – year: 1990 ident: 10.1016/j.aml.2025.109455_b3 |
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| SubjectTerms | Discontinuous nonlinearity Multiple solution Neumann problem Nonsmooth analysis |
| Title | Elliptic Neumann problems with highly discontinuous nonlinearities |
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