Duality theory for linear n -th order integro-differential operators with domain in L m p determined by interface side conditions

Richard C. Brown; Milan Tvrdý; Otto Vejvoda

Czechoslovak Mathematical Journal (1982)

  • Volume: 32, Issue: 2, page 183-196
  • ISSN: 0011-4642

How to cite

top

Brown, Richard C., Tvrdý, Milan, and Vejvoda, Otto. "Duality theory for linear $n$-th order integro-differential operators with domain in $L^p_m$ determined by interface side conditions." Czechoslovak Mathematical Journal 32.2 (1982): 183-196. <http://eudml.org/doc/13305>.

@article{Brown1982,
author = {Brown, Richard C., Tvrdý, Milan, Vejvoda, Otto},
journal = {Czechoslovak Mathematical Journal},
keywords = {duality theory; integro-differential operators; adjoint; interface boundary value problems},
language = {eng},
number = {2},
pages = {183-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Duality theory for linear $n$-th order integro-differential operators with domain in $L^p_m$ determined by interface side conditions},
url = {http://eudml.org/doc/13305},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Brown, Richard C.
AU - Tvrdý, Milan
AU - Vejvoda, Otto
TI - Duality theory for linear $n$-th order integro-differential operators with domain in $L^p_m$ determined by interface side conditions
JO - Czechoslovak Mathematical Journal
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 2
SP - 183
EP - 196
LA - eng
KW - duality theory; integro-differential operators; adjoint; interface boundary value problems
UR - http://eudml.org/doc/13305
ER -

References

top
  1. R. C. Brown, A. M. Krall, n -th order ordinary differential systems under Stieltjes boundary conditions, Czech. Math. J. 27 (102) (1977), 119-131. (1977) Zbl0369.34006MR0430394
  2. R. C. Brown, M. Tvrdý, Generalized boundary value problems with abstract side conditions and their adjoints I, Czech. Math. J., 30 (105) (1980), 7-27. (1980) MR0565904
  3. R. N. Bryan, A nonhomogeneous linear differential system with interface conditions, Proc. AMS 22 (1969), 270-276. (1969) Zbl0201.11002MR0241739
  4. E. A. Coddington, A. Dijksma, Adjoint subspaces in Banach spaces with applications to ordinary differential subspaces, Annali di Mat. Рurа ed Appl., CXVIII (1978), 1 - 118. (1978) Zbl0408.47035MR0533601
  5. R. Conti, 10.1016/0022-0396(68)90045-4, J. Diff. Eq. 4 (1968), 4-11. (1968) Zbl0157.14104MR0218642DOI10.1016/0022-0396(68)90045-4
  6. A. Gonelli, Un teorema di esistenza per un problema di tipo interface, Le Matematiche, 22 (1967), 203-211. (1967) MR0240380
  7. K. Jörgens, Lineare Integraloperatoren, В. G. Teubner Stuttgart, 1970. (1970) MR0461049
  8. J. L. Kelley, I. Namioka, Linear Topological Spaces, Van Nostrand, Princeton, New Jersey, 1963. (1963) Zbl0115.09902MR0166578
  9. A. M. Krall, 10.1016/0022-0396(68)90019-3, J. Diff. Eq. 4 (1968), 327-336. (1968) Zbl0165.42702MR0230968DOI10.1016/0022-0396(68)90019-3
  10. V. P. Maksimov, The property of being Noetherian of the general boundary value problem for a linear functional differential equation, (in Russian), Diff. Urav. 10 (1974), 2288-2291. (1974) MR0361355
  11. V. P. Maksimov, L. F. Rahmatullina, A linear functional-differential equation that is solved with respect to the derivative, (in Russian) Diff. Urav. 9 (1973), 2231-2240. (1973) MR0333397
  12. I. P. Natanson, Theory of Functions of a Real Variable, Frederick Ungar, New York. MR0067952
  13. J. V. Parhimovič, Multipoint boundary value problems for linear integro-differential equations in the class of smooth functions, (in Russian), Diff. Urav. 8 (1972), 549-552. (1972) MR0298370
  14. J. V. Parhimovič, The index and normal solvability of a multipoint boundary value problem for an integro-differential equation, (in Russian), Vesci Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, 1972, 91-93. (1972) MR0305154
  15. Št. Schwabik, Differential equations with interface condtions, Časopis pěst. mat. 105 (1980), 391-408. (1980) MR0597916
  16. Št. Schwabik M. Tvrdý, O. Vejvoda, Differential and Integral Equations: Boundary Value Problems and Ajoints, Academia, Praha, 1979. (1979) MR0542283
  17. F. W. Stallard, Differential systems with interface conditions, Oak Ridge Nat. Lab. Publ. No. 1876 (Physics). 
  18. M. Tvrdý, Linear functional-differential operators: normal solvability and adjoints, Colloquia Mathematica Soc. János Bolyai, 15, Differential Equations, Keszthely (Hungary), 1975, 379-389. (1975) MR0482357
  19. M. Tvrdý, Linear boundary value type problems for functional-differential equations and their adjoints, Czech. Math. J. 25 (100), (1975), 37-66. (1975) MR0374609
  20. M. Tvrdý, Boundary value problems for generalized linear differential equations and their adjoints, Czech. Math. J. 23 (98) (1973), 183-217. (1973) MR0320417
  21. A Zettl, 10.1137/0116069, SIAM J. Appl. Math. 16 (1968), 851-859. (1968) Zbl0162.11201MR0234049DOI10.1137/0116069

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.