Dusan D. Repovs
We study the degenerate elliptic equation
in a bounded open set with homogeneous Neumann boundary condition, where and f has a linear growth. The main result establishes the existence of real numbers and such that the problem has at least two solutions if , there is at least one solution if , and no solution exists for all . The proof combines a priori estimates with topological degree arguments.
Submitted July 20, 2017. Published February 6, 2018.
Math Subject Classifications: 35J65, 35J25, 58E07.
Key Words: Ambrosetti-Prodi problem; degenerate potential; topological degree; anisotropic continuous media.
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| Dusan D. Repovs |
Faculty of Education and Faculty of Mathematics and Physics
University of Ljubljana
SI-1000 Ljubljana, Slovenia
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