Ambrosetti-Prodi problem with degenerate potential and Neumann boundary conditionRepovš, Dušan (Avtor) Ambrosetti-Prodi problemdegenerate potentialtopological degreeanisotropic continuous mediaWe 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.20182019-09-03 12:09:37Članek v reviji109446sl