A variable exponent diffusion problem of concave-convex nature
We deal with the problem (formula presented) Where Ω ⊂ ℝN is a bounded smooth domain, λ > 0 is a parameter and the exponent q(x) is a continuous positive function that takes values both greater than and less than one in Ω. It is therefore a kind of concave-convex problem where the presence of...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_12303429_v47_n2_p613_GarciaMelian |
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todo:paper_12303429_v47_n2_p613_GarciaMelian2023-10-03T16:09:09Z A variable exponent diffusion problem of concave-convex nature García-Melián, J. Rossi, J.D. de Lis, J.C.S. A priori bounds Concave-convex Leray–Schauder degree Minimal solution Variable exponent We deal with the problem (formula presented) Where Ω ⊂ ℝN is a bounded smooth domain, λ > 0 is a parameter and the exponent q(x) is a continuous positive function that takes values both greater than and less than one in Ω. It is therefore a kind of concave-convex problem where the presence of the interphase q = 1 in Ω poses some new diffculties to be tackled. The results proved in this work are the existence of λ* > 0 such that no positive solutions are possible for λ > λ*, the existence and structural properties of a branch of minimal solutions, uλ, 0 < λ < λ*, and, finally, the existence for all λ ∊ (0; λ*) of a second positive solution. © 2016 Juliusz Schauder Centre for Nonlinear Studies. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_12303429_v47_n2_p613_GarciaMelian |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
A priori bounds Concave-convex Leray–Schauder degree Minimal solution Variable exponent |
| spellingShingle |
A priori bounds Concave-convex Leray–Schauder degree Minimal solution Variable exponent García-Melián, J. Rossi, J.D. de Lis, J.C.S. A variable exponent diffusion problem of concave-convex nature |
| topic_facet |
A priori bounds Concave-convex Leray–Schauder degree Minimal solution Variable exponent |
| description |
We deal with the problem (formula presented) Where Ω ⊂ ℝN is a bounded smooth domain, λ > 0 is a parameter and the exponent q(x) is a continuous positive function that takes values both greater than and less than one in Ω. It is therefore a kind of concave-convex problem where the presence of the interphase q = 1 in Ω poses some new diffculties to be tackled. The results proved in this work are the existence of λ* > 0 such that no positive solutions are possible for λ > λ*, the existence and structural properties of a branch of minimal solutions, uλ, 0 < λ < λ*, and, finally, the existence for all λ ∊ (0; λ*) of a second positive solution. © 2016 Juliusz Schauder Centre for Nonlinear Studies. |
| format |
JOUR |
| author |
García-Melián, J. Rossi, J.D. de Lis, J.C.S. |
| author_facet |
García-Melián, J. Rossi, J.D. de Lis, J.C.S. |
| author_sort |
García-Melián, J. |
| title |
A variable exponent diffusion problem of concave-convex nature |
| title_short |
A variable exponent diffusion problem of concave-convex nature |
| title_full |
A variable exponent diffusion problem of concave-convex nature |
| title_fullStr |
A variable exponent diffusion problem of concave-convex nature |
| title_full_unstemmed |
A variable exponent diffusion problem of concave-convex nature |
| title_sort |
variable exponent diffusion problem of concave-convex nature |
| url |
http://hdl.handle.net/20.500.12110/paper_12303429_v47_n2_p613_GarciaMelian |
| work_keys_str_mv |
AT garciamelianj avariableexponentdiffusionproblemofconcaveconvexnature AT rossijd avariableexponentdiffusionproblemofconcaveconvexnature AT delisjcs avariableexponentdiffusionproblemofconcaveconvexnature AT garciamelianj variableexponentdiffusionproblemofconcaveconvexnature AT rossijd variableexponentdiffusionproblemofconcaveconvexnature AT delisjcs variableexponentdiffusionproblemofconcaveconvexnature |
| _version_ |
1807323369503195136 |