Electron. J. Differential Equations,
Vol. 2018 (2018), No. 41, pp. 110.
AmbrosettiProdi problem with degenerate potential and Neumann
boundary condition
Dusan D. Repovs
Abstract:
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: AmbrosettiProdi 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
SI1000 Ljubljana, Slovenia
email: dusan.repovs@guest.arnes.si

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