Quasilinear elliptic problems interacting with its asymptotic spectrum
Under suitable assumptions on the coefficients of the matrix A(x,u) and on the nonlinear term f(x,u), we study the quasilinear problem in bounded domains Ω⊂RN−div(A(x,u)∇u)=f(x,u),x∈Ω,u=0,x∈∂Ω.We extend the semilinear results of Landesman–Lazer (J. Math. Mech. 19 (1970) 609) and of Ambrosetti–Prodi...
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| Aineistotyyppi: | info:eu-repo/semantics/article |
| Kieli: | English |
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Elsevier
2012
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| Aiheet: | |
| Linkit: | http://hdl.handle.net/10835/580 |
| _version_ | 1789406476798787584 |
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| author | Arcoya, David Carmona Tapia, José |
| author_facet | Arcoya, David Carmona Tapia, José |
| author_sort | Arcoya, David |
| collection | DSpace |
| description | Under suitable assumptions on the coefficients of the matrix A(x,u) and on the nonlinear term f(x,u), we study the quasilinear problem in bounded domains Ω⊂RN−div(A(x,u)∇u)=f(x,u),x∈Ω,u=0,x∈∂Ω.We extend the semilinear results of Landesman–Lazer (J. Math. Mech. 19 (1970) 609) and of Ambrosetti–Prodi (in: A Primer on Nonlinear Analysis, Cambridge University Press, Cambridge, 1993) for resonant problems. The existence of positive solution is also considered extending to the quasilinear case the classical result by Ambrosetti–Rabinowitz (J. Funct. Anal. 14 (1973) 349). In this case, the result is obtained as a corollary of the previous multiplicity result in the Ambrosetti–Prodi framework. Keywords: Quasilinear elliptic equations; Bifurcation theory; Resonance; Jumping nonlinearities |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-580 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2012 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-5802023-04-12T19:37:38Z Quasilinear elliptic problems interacting with its asymptotic spectrum Arcoya, David Carmona Tapia, José Mathematics Under suitable assumptions on the coefficients of the matrix A(x,u) and on the nonlinear term f(x,u), we study the quasilinear problem in bounded domains Ω⊂RN−div(A(x,u)∇u)=f(x,u),x∈Ω,u=0,x∈∂Ω.We extend the semilinear results of Landesman–Lazer (J. Math. Mech. 19 (1970) 609) and of Ambrosetti–Prodi (in: A Primer on Nonlinear Analysis, Cambridge University Press, Cambridge, 1993) for resonant problems. The existence of positive solution is also considered extending to the quasilinear case the classical result by Ambrosetti–Rabinowitz (J. Funct. Anal. 14 (1973) 349). In this case, the result is obtained as a corollary of the previous multiplicity result in the Ambrosetti–Prodi framework. Keywords: Quasilinear elliptic equations; Bifurcation theory; Resonance; Jumping nonlinearities 2012-01-03T09:44:46Z 2012-01-03T09:44:46Z 2003-03 info:eu-repo/semantics/article David Arcoya, José Carmona, Quasilinear elliptic problems interacting with its asymptotic spectrum, Nonlinear Analysis: Theory, Methods & Applications, Volume 52, Issue 6, March 2003, Pages 1591-1616, ISSN 0362-546X, 10.1016/S0362-546X(02)00274-2. 0362-546X http://hdl.handle.net/10835/580 en http://www.sciencedirect.com/science/article/pii/S0362546X02002742 info:eu-repo/semantics/openAccess Elsevier |
| spellingShingle | Mathematics Arcoya, David Carmona Tapia, José Quasilinear elliptic problems interacting with its asymptotic spectrum |
| title | Quasilinear elliptic problems interacting with its asymptotic spectrum |
| title_full | Quasilinear elliptic problems interacting with its asymptotic spectrum |
| title_fullStr | Quasilinear elliptic problems interacting with its asymptotic spectrum |
| title_full_unstemmed | Quasilinear elliptic problems interacting with its asymptotic spectrum |
| title_short | Quasilinear elliptic problems interacting with its asymptotic spectrum |
| title_sort | quasilinear elliptic problems interacting with its asymptotic spectrum |
| topic | Mathematics |
| url | http://hdl.handle.net/10835/580 |
| work_keys_str_mv | AT arcoyadavid quasilinearellipticproblemsinteractingwithitsasymptoticspectrum AT carmonatapiajose quasilinearellipticproblemsinteractingwithitsasymptoticspectrum |