Existence results on the semiinfinite interval for first and second order integrodifferential equations in Banach spaces with nonlocal conditions

Mouffak Benchohra; Sotiris K. Ntouyas

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2002)

  • Volume: 41, Issue: 1, page 13-19
  • ISSN: 0231-9721

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Benchohra, Mouffak, and Ntouyas, Sotiris K.. "Existence results on the semiinfinite interval for first and second order integrodifferential equations in Banach spaces with nonlocal conditions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 41.1 (2002): 13-19. <http://eudml.org/doc/23729>.

@article{Benchohra2002,
author = {Benchohra, Mouffak, Ntouyas, Sotiris K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Banach spaces; initial value problems; semilinear integrodifferential equations; mild solution; semiinfinite interval; fixed point},
language = {eng},
number = {1},
pages = {13-19},
publisher = {Palacký University Olomouc},
title = {Existence results on the semiinfinite interval for first and second order integrodifferential equations in Banach spaces with nonlocal conditions},
url = {http://eudml.org/doc/23729},
volume = {41},
year = {2002},
}

TY - JOUR
AU - Benchohra, Mouffak
AU - Ntouyas, Sotiris K.
TI - Existence results on the semiinfinite interval for first and second order integrodifferential equations in Banach spaces with nonlocal conditions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2002
PB - Palacký University Olomouc
VL - 41
IS - 1
SP - 13
EP - 19
LA - eng
KW - Banach spaces; initial value problems; semilinear integrodifferential equations; mild solution; semiinfinite interval; fixed point
UR - http://eudml.org/doc/23729
ER -

References

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  1. Benchohra M., Ntouyas S. K., Existence of mild solutions on semiinfinite intervаl for first order differentiаl equаtions with nonlocаl conditions, Comment. Math. Univ. Carolin. 41 (2000), 485-491. MR1795080
  2. Benchohra M., Ntouyas S. K., Existence of mild solutions on semiinfinite intervаl for second order differentiаl equаtions with nonlocаl conditions, Comment. Math. Prace Mat. 16 (2001), 41-49. MR1876709
  3. Byszewski L., Theorems аbout the existence аnd uniqueness of solutions of а semilineаr evolution nonlocаl Cаuchy problem, J. Math. Anal. Appl. 162 (1991), 494-505. (1991) MR1137634
  4. Corduneanu C., Integral Equations and Applications, Cаmbridge Univ. Press, New York, 1990. (1990) MR1109491
  5. Dugundji J., Granas A., Fixed Point Theory, Monogrаfie Mаt. PWN, Wаrsаw, 1982. (1982) Zbl0483.47038MR0660439
  6. Fattorini H. O., Second order linear differential equations in Banach spaces, North-Hollаnd Mаthemаticаl Studies, Vol. 108, North-Hollаnd, Amsterdаm, 1985. (1985) Zbl0564.34063MR0797071
  7. Ghisi M., Mild solutions of evolution equаtions аnd meаsures of noncompаctness, Nonlinear Anal. 26, 7 (1996), 1193-1205. (1996) MR1376098
  8. Goldstein J. A., Semigroups of Linear Operators and Applications, Oxford, New York, 1985. (1985) Zbl0592.47034MR0790497
  9. Heikkila S., Lakshmikantham V., Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Mаrcel Dekker, New York, 1994. (1994) MR1280028
  10. Heikkila S., Lakshmikantham V., On mild solutions of first order discontinuous semilineаr differentiаl equаtions in Bаnаch Spаces, Applic. Anal. 56, 1-2 (1995), 131-146. (1995) MR1378017
  11. Ladas G., Lakshmikantham V., Differential Equatiоns in Abstract Spaces, Acаdemic Press, New York, London, 1972. (1972) 
  12. Lakshmikantham V., Leela S., Existence аnd monotone rnethod for periodic solutions of first order differentiаl equаtions, J. Math. Anal. Appl. 91 (1983), 237-243. (1983) MR0688542
  13. Pazy A., Semigrоups оf Linear Operatоrs and Applicatiоns tо Partial Differential Equatiоns, Springer-Verlаg, New York, 1983. (1983) MR0710486
  14. Travis C. C., Webb G. F., Second order differentiаl equаtions in Bаnаch spаces, Prоc. Int. Symp. оn Nоnlinear Equatiоns in Abstract Spaces, Academic Press, New Yоrk (1978), 331-361. (1978) MR0502551
  15. Travis C. C., Webb G. F., Cosine fаmilies аnd аbstrаct nonlineаr second order differentiаl equаtions, Acta Math. Hungar. 32 (1978), 75-96. (1978) MR0499581
  16. Yоsida K., Functiоnal Analysis, бth edn. Springer-Verlаg, Berlin, 1980. (1980) 

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