20.500.12556/RUL-108788 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 unilateral growth constant sign and nodal solutions multiplicity theorems critical groups true false true Angleški jezik Ni določen Članek v reviji 2019-07-25 10:30:43 2019-07-25 10:30:45 2022-08-20 03:48:33 0000-00-00 00:00:00 2019 0 0 Str. 319-340 iss. 2 Vol. 31 2019 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956.2 0933-7741 10.1515/forum-2018-0114 18471257 26801408 RAZ_Papageorgiou_Nikolaos_i2019.pdf RAZ_Papageorgiou_Nikolaos_i2019.pdf 1 BF18BDDC8498C4D684D7F0C52BB9D107 241daeeafd39d7204d1e43079e8b75d453b3bb847736320a7aef925350204ac1 cfc4fe1a-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=120754 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0