Geodesic
On Coefficients of Eigenfunction Expansions for Boundary-Value Problems with Parameter in Boundary Conditions
Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 493-506

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In this paper, we consider boundary-value problems for an $n$th-order ordinary differential equation with polynomials of the spectral parameter in the equation and in the boundary conditions. For a wide class of such problems, we find coefficients of the eigen and associated function expansions for the Shkalikov linearizer. 
@article{MZM_2004_75_4_a1,
     author = {A. M. Akhtyamov},
     title = {On {Coefficients} of {Eigenfunction} {Expansions} for {Boundary-Value} {Problems} with {Parameter} in {Boundary} {Conditions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {493--506},
     publisher = {mathdoc},
     volume = {75},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a1/}
}
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A. M. Akhtyamov. On Coefficients of Eigenfunction Expansions for Boundary-Value Problems with Parameter in Boundary Conditions. Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 493-506. http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a1/