Spectral properties of some semi-elliptic operators in L-p spaces

Spectral properties of the semi- elliptic operator in A(mu)U = partial derivative(2)U/partial derivative x(1)(2) + partial deriva tive(4)U/partial derivative x(2)(4) + mu/eta(2)(x(1)) U in L-p (1 < p < infinity) spaces are investigated. In particular it is prov ed that there exists mu(0) such that if mu > mu(0), then A(mu),(p) has the point spectrum and lambda(k)(A(mu,p)) similar to k(4/3), where A(mu,p) is t he unbounded operator generated by A(mu) in L-p and lambda(k)(A(mu,p)) its eigenvalues.