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,ω,α,β are real-valued functions and satisfy basic condition p(x)>0,ω(x)≠0 a.e.x ∈[-1,1].1/p,q,ω,α.β∈L1[-1,1],ω(x)changes its sign on[-1,1],λ is a spectral parameter,and 01,02 ∈[0,π).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,ω、α,β are real-valued functions and satisfy basic condition p(x)>0,ω(x)≠0 a.e.x∈[0,1].1/p,q,ω,α,β∈L1[0,1],u.4x)changes its sign on[0,1],λ is a spectral parameter,and01,02∈[0,π),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,ω,are real-valued functions and satisfy basic condition p(x)>0.ω(x)≠ 0 a.e.x ∈[O,T],1/p.q,ω∈L1[0,T]ω(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.