Spectral analysis of eigenvalue problem with the (p(x),q(x))-Laplacian

Abstract

In this study, a spectral problem that involves the Robin (a(x),b(x))-Laplacian on a bounded domain in Rⁿ is analyzed. With the help of the  Ljusternik-Schnirelmann principle, it is established that an increasing sequence of eigenvalues exists.  Using the min-max principle, we also established that  the infimum of the spectrum is zero, and all the eigenvalues are non-negative. It was further proved that there exists a principal eigenvalue for this problem and that the spectrum is open.