HALF-LINEAR EIGENVALUE PROBLEMS

We consider the eigenvalue problem x ''/x'/(n-1) [lambda(n+1) q(t)+/l ambda/(mu)g(t)] x(n)=0, Uj(x)=0,j=1,2, for t is an element of[0, b], where a(n)=/a/(n) sgn a, a is an element of IR, lambda is an element of IR, the constants mu, nu are real such that 0 less than or equal to mu<n and derive asymptotic estimates for solutions of the differentia l equation in the definite case q(t)>0 which corresponds to the well-k nown WKB-approximation in the linear case n=1, mu=0. In the second par t we investigate the asymptotic distribution of the eigenvalues in the general case of two-point boundary conditions and refine these result s for the so called separated boundary conditions.