Double-phase problems with reaction of arbitrary growth
We consider a parametric nonlinear nonhomogeneous elliptic equation, driven by the sum of two differential operators having different structure. The associated energy functional has unbalanced growth and we do not impose any global growth conditions to the reaction term, whose behavior is prescribed only near the origin. Using truncation and comparison techniques and Morse theory, we show that the problem has multiple solutions in the case of high perturbations. We also show that if a symmetry condition is imposed to the reaction term, then we can generate a sequence of distinct nodal solutions with smaller and smaller energies.
2018
2019-08-23 13:05:31
1033
double-phase problem, nonlinear maximum principle, nonlinear regularity theory, critical point theory, critical groups
dk_c
Nikolaos
Papageorgiou
70
Vicenţiu
Rǎdulescu
70
Dušan
Repovš
70
UDK
4
517.956.2
ISSN pri članku
9
0044-2275
DOI
15
10.1007/s00033-018-1001-2
COBISS_ID
3
18409561
OceCobissID
13
26662656
RAZ_Papageorgiou_Nikolaos_Socrates_i2018.pdf
665561
Predstavitvena datoteka
2019-08-23 13:08:20