# Some properties of eigenfunctions of linear pencils and applications to mixed type operator-differential equations

Banach Center Publications (1992)

- Volume: 27, Issue: 2, page 373-382
- ISSN: 0137-6934

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topPyatkov, S.. "Some properties of eigenfunctions of linear pencils and applications to mixed type operator-differential equations." Banach Center Publications 27.2 (1992): 373-382. <http://eudml.org/doc/262693>.

@article{Pyatkov1992,

abstract = {In the first part of the paper we study some properties of eigenelements of linear selfadjoint pencils Lu = λBu. In the second part we apply these results to the investigation of some boundary value problems for mixed type second order operator-differential equations.},

author = {Pyatkov, S.},

journal = {Banach Center Publications},

keywords = {properties of eigenelements of linear selfadjoint pencils; boundary value problems for mixed type second order operator-differential equations},

language = {eng},

number = {2},

pages = {373-382},

title = {Some properties of eigenfunctions of linear pencils and applications to mixed type operator-differential equations},

url = {http://eudml.org/doc/262693},

volume = {27},

year = {1992},

}

TY - JOUR

AU - Pyatkov, S.

TI - Some properties of eigenfunctions of linear pencils and applications to mixed type operator-differential equations

JO - Banach Center Publications

PY - 1992

VL - 27

IS - 2

SP - 373

EP - 382

AB - In the first part of the paper we study some properties of eigenelements of linear selfadjoint pencils Lu = λBu. In the second part we apply these results to the investigation of some boundary value problems for mixed type second order operator-differential equations.

LA - eng

KW - properties of eigenelements of linear selfadjoint pencils; boundary value problems for mixed type second order operator-differential equations

UR - http://eudml.org/doc/262693

ER -

## References

top- [1] R. Beals, Indefinite Sturm-Liouville problems and half-range completeness, J. Differential Equations 56 (1985), 391-407. Zbl0512.34017
- [2] I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, Nauka, Moscow 1965 (in Russian); English transl.: Amer. Math. Soc., Providence, R.I., 1969.
- [3] N. V. Kislov, Inhomogeneous boundary value problem for a second order operator-differential equation, Dokl. Akad. Nauk SSSR 280 (1985), 1055-1058 (in Russian); English transl. in Soviet Math. Dokl.
- [4] N. V. Kislov, Boundary value problems for second order operator-differential equations of Tricomi type, Differentsial'nye Uravneniya 11 (1975), 718-720 (in Russian); English transl. in Differential Equations 11 (1975).
- [5] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. 1, Springer, Berlin 1972.
- [6] S. G. Pyatkov, Properties of eigenfunctions of a spectral problem and their applications, in: Well-Posed Boundary Value Problems for Nonclassical Equations of Mathematical Physics, Institute of Mathematics, Novosibirsk 1984, 115-130 (in Russian).
- [7] S. G. Pyatkov, On the solvability of a boundary value problem for a parabolic equation with changing time direction, Soviet Math. Dokl. 32 (1985), 895-897. Zbl0605.35046
- [8] S. G. Pyatkov, Properties of eigenfunctions of a spectral problem and their applications, in: Some Applications of Functional Analysis to Problems of Mathematical Physics, Institute of Mathematics, Novosibirsk 1986, 65-85 (in Russian).
- [9] S. G. Pyatkov, Solvability of boundary value problems for second order mixed type equations, in: Nonclassical Partial Differential Equations, Institute of Mathematics, Novosibirsk 1988, 77-90 (in Russian). Zbl0825.35083
- [10] S. G. Pyatkov, Some properties of eigenfunctions of linear sheaves, Siberian Math. J. 30 (1989), 587-597. Zbl0759.47013
- [11] A. A. Shkalikov and V. T. Pliev, Compact perturbations of strongly damped pencils of operators, Mat. Zametki 45 (1989), 118-128 (in Russian). Zbl0677.47011
- [12] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag Wiss., Berlin 1977, and North-Holland, Amsterdam 1978. Zbl0387.46033

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