Eigenvalues of a class of regular fourth-order Sturm-Liouville problems (Q440951)

The paper deals with the eigenvalue problem for the fourth-order Sturm-Liouville equation NEWLINE\[NEWLINE(p(x)y'')''+ q(x)y = \lambda w(x)y NEWLINE\]NEWLINE with boundary conditions NEWLINE\[NEWLINE A\left[ y(a),y'(a) ,(py'')(a) , (py'')'(a) \right]^{\top}+ B\left[ y(b),y'(b),(py'')(b), (py'')'(b) \right]^{\top}=\left[ 0, 0,0 , 0 \right]^{\top}.NEWLINE\]NEWLINE The authors study separated and coupled conditions. It is shown that the eigenvalues are differentiable functions of all parameters, i.e., the endpoints \(a, b\), the boundary conditions \(A, B\), the coefficients \(p, q\) and the weight function \(w\).