TY - JOUR
AU - García-Melián, J.
AU - Rossi, J.D.
AU - de Lis, J.C.S.
T1 - A variable exponent diffusion problem of concave-convex nature
LA - eng
PY - 2016
SP - 613
EP - 639
T2 - Topological Methods in Nonlinear Analysis
SN - 1230-3429
VL - 47
IS - 2
PB - Juliusz Schauder Center for Nonlinear Studies
PP - Torun
AB - 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.
DO - 10.12775/TMNA.2016.019
UR - https://portalciencia.ull.es/documentos/5e3c3bd129995246bbf6039b
DP - Dialnet - Portal de la Investigación
ER -