20.500.12556/RUL-108776 Nonlinear nonhomogeneous boundary value problems with competition phenomena We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave) contribution coming from the parametric boundary (source) term. We show that for all small parameter values ▫$\lambda > 0$▫, the problem has at least five nontrivial smooth solutions, four of constant sign and one nodal. We also produce extremal constant sign solutions and determine their monotonicity and continuity properties as the parameter ▫$\lambda > 0$▫ varies. In the semilinear case we produce a sixth nontrivial solution but without any sign information. Our approach uses variational methods together with truncation and perturbation techniques, and Morse theory. nonlinear nonhomogeneous differential operator nonlinear boundary condition nonlinear regularity theory nonlinear maximum principle critical groups true false true Angleški jezik Ni določen Članek v reviji 2019-07-23 08:10:49 2019-07-23 08:10:53 2022-08-20 03:48:28 0000-00-00 00:00:00 2019 0 0 Str. 251-298 iss. 1 Vol. 80 Aug. 2019 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956.2 0095-4616 10.1007/s00245-017-9465-6 18194265 24984064 RAZ_Papageorgiou_Nikolaos_i2019.pdf RAZ_Papageorgiou_Nikolaos_i2019.pdf 1 A427F0BD10931603438329D950338F57 775e7115fb1efd9c246cd38d0d5ae49ec7ae90f2bfac9945dd18bde8b78173b1 cfa927bf-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=120751 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0