Estimates On The Non-real Eigenvalues Of Fourth Order Indefinite Differential Operators

The present paper gives a estimate on the non-real eigenvalues for a class of fourth order differential operators.Using operator theory and classical analysis,we study the eigenvalue problem for indefinite differential operators when weight function changes sign,and discuss the case of multiple turning points and a turning point for the weight function,then,we obtain the estimates of the real and imaginary parts of the non-real eigenvalues that are related to the weight function and independent of the weight function.