Two Term Asymptotics of Counting Function for One Dimensional p-Laplace Operator with Mixed and Periodic Boundary-value Conditions

1 Main Results Let Ω(?) R be a non-empty open subset with finite Lebesgue measure |Ω|1 and boundary Г= σΩ. We can write Ωas the union of its connected components, i.e., Ω= ∪Ij, where the open intervals Ij are pairwise disjoint and of length lj,. Since |Ω|1= sum from j=1 to ∞lj < +00, we can assume, without loss of generality, that l1 ≥l2 ≥…≥lk ≥…> 0. In this paper, we consider the eigenvalue problem of the p-Laplace operator with mixed boundary-value conditions, i.e.,