Non-real Eigenvalues Of Some Classes Of Boundary Value Problems With Indefinite Weight

In this thesis,we study the non-real half-eigenvalues of half-linear problems with sign-changing weight and the non-real eigenvalues of second order indefinite linear periodic boundary value problem.The main results are:In the first chapter,we consider the non-real half-eigenvalues of second-order indefinite half-linear boundary value problem(?)where p,q,?,?,? are real-valued functions and satisfy basic condition p(x)>0,?(x)?0 a.e.x ?[-1,1].1/p,q,?,?.??L1[-1,1],?(x)changes its sign on[-1,1],? is a spectral parameter,and 01,02 ?[0,?).We obtain the priori bounds estimation for possible non-real eigenvalues and a sufficient condition for the existence of non-real eigenvalues.In the second chapter,we consider the non-real half-eigenvalues of second-order indefinite half-linear boundary value problem(?)where p,q,???,? are real-valued functions and satisfy basic condition p(x)>0,?(x)?0 a.e.x?[0,1].1/p,q,?,?,??L1[0,1],u.4x)changes its sign on[0,1],? is a spectral parameter,and01,02?[0,?),y±=max{±y(x),0}.We obtain the priori bounds estimation for possible non-real eigen-values and a sufficient condition for the existence and non-existence of non-real eigenvalues,and the properties of half-characteristic curve.In the third chapter,we consider non-real eigenvalues of second-order linear indefinite periodic boundary value problem(?)wherep,q,?,are real-valued functions and satisfy basic condition p(x)>0.?(x)? 0 a.e.x ?[O,T],1/p.q,??L1[0,T]?(x)changes its sign on[0,T],A is a spectral parameter.We obtain the priori bounds estimation for possible non-real eigenvalues and a sufficient condition for the existence of non-real eigenvalues.