Existence and regularity results for a degenerate elliptic nonlinear equation on weighted Sobolev spaces

Abstract

This paper deals with the existence of many solutions a degenerate weighted elliptic equation which its the number of solutions depend  on degeneracy term a i.e., the number of subdomains of Ω\a ⁻¹ (0) whose boundary is made by submanifolds with 1-codimension.  Moreover, by the Ljusternik-Schnirelman principle, we would study the corresponding eigenvalue problem and obtained the nonnegative eigenvalues sequence of main problem. Finally, we will discuss of the regularity of the solutions on C ¹,α(Ω).