Non-linear Neumann weighted eigenvalues in outward cuspidal domains

Abstract: In this article we study the non-linear Neumann spectral problem in outward cuspidal domains. By using composition operators we prove embedding of Sobolev spaces into weighted Lebesgue spaces. As a consequence, we obtain solvability of the Neumann spectral problem and estimates of Neumann weighted eigenvalues in outward cuspidal domains.