GENERALIZED EIGENVALUES OF THE (P, 2)-LAPLACIAN UNDER A PARAMETRIC BOUNDARY CONDITION

In this paper we study a general eigenvalue problem for the so called (p, 2)-Laplace operator on a smooth bounded domain Omega subset of R-N under a nonlinear Steklov type boundary condition, namely {-Delta(p)u - Delta u = lambda a(X)u in Omega, (vertical bar del u vertical bar(p-2) + 1)partial derivative u/partial derivative v = lambda b(x)u on partial derivative Omega. For positive weight functions a and b satisfying appropriate integrability and boundedness assumptions, we show that, for all p > 1, the eigenvalue set consists of an isolated null eigenvalue plus a continuous family of eigenvalues located away from zero.