Chow-Lasota Theorem for BVPs of Evolution Equations

Giovanni Vidossich

Bollettino dell'Unione Matematica Italiana (2010)

  • Volume: 3, Issue: 2, page 325-335
  • ISSN: 0392-4041

Abstract

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We extend the main result of CHOW-LASOTA [1] to evolution equations and show some applications of the outcome.

How to cite

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Vidossich, Giovanni. "Chow-Lasota Theorem for BVPs of Evolution Equations." Bollettino dell'Unione Matematica Italiana 3.2 (2010): 325-335. <http://eudml.org/doc/290656>.

@article{Vidossich2010,
abstract = {We extend the main result of CHOW-LASOTA [1] to evolution equations and show some applications of the outcome.},
author = {Vidossich, Giovanni},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {325-335},
publisher = {Unione Matematica Italiana},
title = {Chow-Lasota Theorem for BVPs of Evolution Equations},
url = {http://eudml.org/doc/290656},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Vidossich, Giovanni
TI - Chow-Lasota Theorem for BVPs of Evolution Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2010/6//
PB - Unione Matematica Italiana
VL - 3
IS - 2
SP - 325
EP - 335
AB - We extend the main result of CHOW-LASOTA [1] to evolution equations and show some applications of the outcome.
LA - eng
UR - http://eudml.org/doc/290656
ER -

References

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  1. CHOW, S. N. - LASOTA, A., On boundary value problems for ordinary differential equations, J. Diff. Eqs., 14 (1973), 326-337. Zbl0285.34009MR330598DOI10.1016/0022-0396(73)90051-X
  2. LASOTA, A., On the existence and uniqueness of solutions of a multipoint boundary value problem, Annales Polon. Math., 38 (1980), 305-310. Zbl0458.34010MR599255DOI10.4064/ap-38-3-305-310
  3. LASOTA, A. - SZAFRANIEC, F. H., On Hammerstein integral equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 59 (1975), 65-67. Zbl0345.45007MR450914
  4. LLOYD, N. G., Degree Theory, Cambridge University Press (Cambridge, 1978). MR493564
  5. LUMER, G. - PHILLIPS, R. S., Dissipative operators in Banach space, Pacific J. Math., 11 (1961), 679-698. Zbl0101.09503MR132403
  6. PAZY, A., A class of semi-linear equations of evolution, Israel J. Math., 20 (1975), 23-36. Zbl0305.47022MR374996DOI10.1007/BF02756753
  7. PAZY, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag (New York, 1983). Zbl0516.47023MR710486DOI10.1007/978-1-4612-5561-1
  8. PICCININI, L. C. - STAMPACCHIA, G. - VIDOSSICH, G., Ordinary Differential Equations in 𝐑 N (Problems and Methods), Springer-Verlag (New York, 1984). Zbl0535.34001MR740539DOI10.1007/978-1-4612-5188-0
  9. VIDOSSICH, G., Differential inequalities for evolution equations, Nonlinear Analysis TMA, 25 (1995), 1063-1069. Zbl0846.34062MR1350729DOI10.1016/0362-546X(95)00101-Z
  10. VIDOSSICH, G., An addition and a correction to my paper "Differential inequalities for evolution equations", Nonlinear Anal. TMA, 72 (2010), 618-623. Zbl1178.47028MR2579329DOI10.1016/j.na.2009.06.112
  11. VIDOSSICH, G., On the continuous dependence of solutions of boundary value problems for ordinary differential equations, J. Diff. Eqs., 82 (1989), 1-14. Zbl0725.34007MR1023298DOI10.1016/0022-0396(89)90164-2
  12. VIDOSSICH, G., Smooth dependence on initial data of mild solutions to evolution equations, Boll. Unione Mat. Ital. (serie 9), 2 (2009), 731-754. Zbl1186.65066MR2569301
  13. WARD, J. R. JR., Boundary value problems for differential equations in Banach space, J. Math. Anal. Appl., 70 (1979), 589-598. Zbl0438.34057MR543596DOI10.1016/0022-247X(79)90067-2
  14. WARD, J. R. JR., Semilinear boundary value problems in Banach space, in "Nonlinear Equations in Abstract Spaces", ed. V. Lakshmikantham, Academic Press (New York, 1978), 469-477. MR502540

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