20.500.12556/RUL-109446 Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition We study the degenerate elliptic equation ▫$$ -\operatorname{div}(|x|^\alpha \nabla u) = f(u) + t\phi(x) + h(x)$$▫ in a bounded open set ▫$\Omega$▫ with homogeneous Neumann boundary condition, where ▫$\alpha \in (0,2)$▫ and ▫$f$▫ has a linear growth. The main result establishes the existence of real numbers and ▫$t^\ast$▫ such that the problem has at least two solutions if ▫$t \leq t_\ast$▫, there is at least one solution if ▫$t_\ast < t \leq t^\ast$▫, and no solution exists for all ▫$t > t^\ast$▫. The proof combines a priori estimates with topological degree arguments. Ambrosetti-Prodi problem degenerate potential topological degree anisotropic continuous media true false true Angleški jezik Ni določen Članek v reviji 2019-09-03 12:09:37 2019-09-03 12:09:38 2022-08-21 03:42:10 0000-00-00 00:00:00 2018 0 0 art. no. 41, str. 1-10 Vol. 2018 2018 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 1072-6691 18249305 7027289 RAZ_Repovs_Dusan_i2018.pdf RAZ_Repovs_Dusan_i2018.pdf 1 DBB154C53F98840B461BD4DF45B26560 b81de5bc8f0291be6cb9190044f95060f9d18ac1720fbeaabe07bcab030d898a deb2721c-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121019 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0