On a non-homogeneous eigenvalue problem involving a potential: an Orlicz-Sobolev space setting. (English) Zbl 1186.35116
Summary: We study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential \(V\). The problem is analyzed in the context of Orlicz-Sobolev spaces. Connected with this problem we also study the optimization problem for the particular eigenvalue given by the infimum of the Rayleigh quotient associated to the problem with respect to the potential \(V\) when \(V\) lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space.
MSC:
| 35P05 | General topics in linear spectral theory for PDEs |
| 35J70 | Degenerate elliptic equations |
| 35J60 | Nonlinear elliptic equations |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
eigenvalue problem; Orlicz-Sobolev space; variable exponent Lebesgue space; optimization problemReferences:
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