Repovs, Dusan D.2022-01-072022-01-072018-02-06Repovs, D. D. (2018). Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition. <i>Electronic Journal of Differential Equations, 2018</i>(41), pp. 1-10.1072-6691https://hdl.handle.net/10877/15097We study the degenerate elliptic equation -div(|x|α∇u) = ƒ(u) + tφ(x) + h(x) in a bounded open set Ω with homogeneous Neumann boundary condition, where α ∈ (0, 2) and ƒ has a linear growth. The main result establishes the existence of real numbers t* and t* such that the problem has at least two solutions if t ≤ t*, there is at least one solution if t* < t ≤ t*, and no solution exists for all t > t*. The proof combines a priori estimates with topological degree arguments.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalAmbrosetti-Prodi problemDegenerate potentialTopological degreeAnisotropic continuous mediaArticle