Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition
Date
2018-02-06
Authors
Repovs, Dusan D.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Ambrosetti-Prodi problem, Degenerate potential, Topological degree, Anisotropic continuous media
Citation
Repovs, 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.