TY - JOUR
AU - Sabina de Lis, J.C.
T1 - Nonlinear flux “concave–convex” problems: a fibering method approach
LA - eng
PY - 2020
SP - 1738
EP - 1753
T2 - Advances in Operator Theory
SN - 2538-225X
VL - 5
IS - 4
PB - Birkhauser
AB - This paper studies the nonlinear flux problem: [Figure not available: see fulltext.] where Δp stands for the p-Laplacian operator, Ω⊂ RN is a bounded smooth domain, λ is a positive parameter and ν stands for the outer unit normal at ∂Ω. The exponents q, r are assumed to vary in the concave convex regime 1 < q< p< r while 1 < p< N and r is subcritical r< p∗. Our objective here is showing the existence, for every 0 < λ< λ¯ , of two different sets of infinitely many solutions of (P). The energy functional associated to the problem exhibits a different sign on each of these sets. The analysis of positive energy solutions involves the so-called fibering method (Drábek and Pohozaev in Proc R Soc Edinb Sect A 127(4):703–726, 1997). Our results have been inspired by similar ones in García-Azorero et al. (J Differ Equ 198(1):91–128, 2004), García-Azorero and Peral (Trans Am Math Soc 323(2):877–895, 1991) and El Hamidi (Commun Pure Appl Anal 3(2):253–265, 2004). This work can be considered as a natural continuation of Sabina de Lis (Differ Equ Appl 3(4):469–486, 2011), Sabina de Lis and Segura de León (Adv Nonlinear Stud 15(1):61–90, 2015) and Sabina de Lis and Segura de León (Nonlinear Anal 113:283–297, 2015). The main achievement of the latter of these works consisted in showing a global existence result of positive solutions to (P).
DO - 10.1007/S43036-020-00092-4
UR - https://portalciencia.ull.es/documentos/5fa289662999524084dd7a26
DP - Dialnet - Portal de la Investigación
ER -