TY  - JOUR
AU  - García-Melián, J.
AU  - Rossi, J.D.
AU  - De Lis, J.C.S.
T1  - A diffusion equation with a variable reaction order
LA  - eng
PY  - 2018
SP  - 555
EP  - 566
T2  - Advanced Nonlinear Studies
SN  - 1536-1365
VL  - 18
IS  - 3
PB  - Walter de Gruyter GmbH
AB  - 
                            This paper deals with the problem (Formula presented) where Ω R
                            N
                             is a bounded smooth domain, λ > 0 is a parameter and the reaction order q(x) is a Hölder continuous positive function satisfying q(x) > 1 for all x ò . The relevant feature here is that q is assumed to achieve the value one on ∂Ω. By assuming that q is subcritical, our main result states the existence of a positive solution for all λ > 0. We also study its asymptotic behavior as λ→ 0 and as λ→ ∞. It should be noticed that the fact that q = 1 somewhere in ∂Ω gives rise to serious difficulties when looking for critical points of the functional associated with the problem above. This work is a continuation of [13] where q is assumed to take values both greater and smaller than one in , but is constrained to satisfy q(x) > 1 on ∂Ω.
                        
DO  - 10.1515/ANS-2017-6030
UR  - https://portalciencia.ull.es/documentos/5e3c3e8429995246bbf611d5
DP  - Dialnet - Portal de la Investigación
ER  -