STEKLOV EIGENVALUES PROBLEMS FOR GENERALIZED (p, q)-LAPLACIAN TYPE OPERATORS

In this paper, we study the following class of (p, q) elliptic problems under Steklov-type boundary conditions {-div (a(vertical bar del u vertical bar(p))vertical bar del u vertical bar(p-2)del u) + a(vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u = 0 in Omega, a(vertical bar del u vertical bar(p))vertical bar del u vertical bar(p-2) del u.v = lambda vertical bar u vertical bar(m-2)u on partial derivative Omega, where Omega is a smooth bounded domain in R-N (N >= 2), nu is the outward unit normal vector on partial derivative Omega, 2 <= p < N, m is an element of R with m > 1 in suitable ranges listed later and a is a C-1 real function and lambda > 0 is a real parameter. Using variational methods, we establish the existence of a continuous and unbounded set of positive generalized eigenvalues.