Nonlinear boundary value problems at resonance for differential equations in Banach spaces

Bogdan Przeradzki

Mathematica Slovaca (1995)

  • Volume: 45, Issue: 2, page 139-153
  • ISSN: 0139-9918

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Przeradzki, Bogdan. "Nonlinear boundary value problems at resonance for differential equations in Banach spaces." Mathematica Slovaca 45.2 (1995): 139-153. <http://eudml.org/doc/32040>.

@article{Przeradzki1995,
author = {Przeradzki, Bogdan},
journal = {Mathematica Slovaca},
keywords = {semilinear equation at resonance; fixed point; Green function; compactness; Banach space},
language = {eng},
number = {2},
pages = {139-153},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Nonlinear boundary value problems at resonance for differential equations in Banach spaces},
url = {http://eudml.org/doc/32040},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Przeradzki, Bogdan
TI - Nonlinear boundary value problems at resonance for differential equations in Banach spaces
JO - Mathematica Slovaca
PY - 1995
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 45
IS - 2
SP - 139
EP - 153
LA - eng
KW - semilinear equation at resonance; fixed point; Green function; compactness; Banach space
UR - http://eudml.org/doc/32040
ER -

References

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  1. CESARI L., Functional analysis, nonlinear differential equations and the alternative method, In: Nonlinear Functional Analysis and Differential Equations (L. Cesari, R. Kannan, J.D. Schuur, eds.), Marcel Dekker Inc., New York, 1976, pp. 1-198. (1976) MR0487630
  2. DALECKIǏ J. L., KREǏN M. G., Stability of Solutions of Differential Equations in Banach Spaces, (Russian), Nauka, Moscov, 1970. (1970) MR0352638
  3. DEFIGUEIREDO D. G., On the range of nonlinear operators with linear asymptotes which are not invertible, Comment. Math. Univ. Carolin. 15 (1974), 415-428. (1974) MR0365254
  4. DRÁBEK P., Landesman-Lazer condition and nonlinearities with linear growth, Czechoslovak Math. J. 40(115) (1990), 70-87. (1990) MR1037351
  5. DUGUNDJI J., GRANAS A., Fixed Point Theory, Vol. I, PWN, Warsaw, 1981. (1981) 
  6. FUČÍK S., Solvability of Nonlinear Equations and Boundary Value Problems, D. Reidel Publ. Comp., Dordrecht, 1980. (1980) MR0620638
  7. FURI M.-PERA P., An elementary approach to boundary value problems at resonance, Nonlinear Anal. 4 (1980), 1081-1089. (1980) Zbl0454.47054MR0591301
  8. IANNACCI R., NKASHAMA M. N., Nonlinear two-point boundary value problems at resonance without Landesman-Lazer condition, Proc. Amer. Math. Soc. 106 (1989), 943-952. (1989) Zbl0684.34025MR1004633
  9. KANNAN R., Perturbation methods for nonlinear problems at resonance, In: Nonlinear Functional Analysis ... (see [1]) pp. 209-226. Zbl0356.34057MR0492478
  10. LANDESMAN E. M., LAZER A. C., Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. (1970) Zbl0193.39203MR0267269
  11. MAWHIN J., Topological degree methods in nonlinear boundary value problems, In: Regional Conf. Series in Math. 40, Amer. Math. Soc., Providence R.I., 1979. (1979) Zbl0414.34025MR0525202
  12. PRZERADZKI B., An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43. (1991) Zbl0746.47043MR1110659
  13. PRZERADZKI B., Operator equations at resonance with unbounded nonlinearities, Preprint. Zbl0881.47045MR1404067
  14. PRZERADZKI B., A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl. 180 (1993), 553-565. (1993) Zbl0807.34029MR1251875
  15. PRZERADZKI B., A note on solutions of semilinear equations at resonance in a cone, Ann. Polon. Math. 58 (1993), 95-103. (1993) Zbl0776.34035MR1215764
  16. PRZERADZKI B., Three methods for the study of semilinear equations at resonance, Colloq. Math. 66 (1993), 109-129. (1993) Zbl0828.47054MR1242650
  17. WILLIAMS S. A., A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586. (1970) Zbl0209.13003MR0267267

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