TY  - JOUR
ID  - Stăncuţ2016
LB  - Stăncuţ2016
AU  - Stăncuţ, Ionela-Loredana
AU  - Stîrcu, Iulia Dorotheea
TI  - Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces
ST  - Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 1
SP  - 81
EP  - 101
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.1.81
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.1.81
AB  - In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential \(V\) on a bounded domain in \(\mathbb{R}^N\) (\(N\geq 3\)) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any \(\lambda\gt 0\) is an eigenvalue of our problem. The second theorem states the existence of a constant \(\lambda_{*}\gt 0\) such that any \(\lambda\in(0,\lambda_{*}]\) is an eigenvalue, while the third theorem claims the existence of a constant \(\lambda^{*}\gt 0\) such that every \(\lambda\in[\lambda^{*}, \infty)\) is an eigenvalue of the problem.
KW  - anisotropic Orlicz-Sobolev space
KW  - potential
KW  - critical point
KW  - weak solution
KW  - eigenvalue
SN  - 1232-9274
ER  -