Nonlinear Dirichlet problems with unilateral growth on the reaction
We consider a nonlinear Dirichlet problem driven by the ▫$p$▫-Laplace differential operator with a reaction which has a subcritical growth restriction only from above. We prove two multiplicity theorems producing three nontrivial solutions, two of constant sign and the third nodal. The two multiplicity theorems differ on the geometry near the origin. In the semilinear case (that is, ▫$p=2$▫), using Morse theory (critical groups), we produce a second nodal solution for a total of four nontrivial solutions. As an illustration, we show that our results incorporate and significantly extend the multiplicity results existing for a class of parametric, coercive Dirichlet problems
2019
2019-07-25 10:30:43
1033
unilateral growth, constant sign and nodal solutions, multiplicity theorems, critical groups
dk_c
Nikolaos S.
Papageorgiou
70
Vicenţiu
Rǎdulescu
70
Dušan
Repovš
70
UDK
4
517.956.2
ISSN pri članku
9
0933-7741
DOI
15
10.1515/forum-2018-0114
COBISS_ID
3
18471257
OceCobissID
13
26801408
RAZ_Papageorgiou_Nikolaos_i2019.pdf
672639
Predstavitvena datoteka
2019-08-28 12:29:07