A topological version of the Ambrosetti-Prodi theorem
Annales Polonici Mathematici (1996)
- Volume: 64, Issue: 2, page 121-130
- ISSN: 0066-2216
Access Full Article
top
Abstract
topHow to cite
topBogdan Przeradzki. "A topological version of the Ambrosetti-Prodi theorem." Annales Polonici Mathematici 64.2 (1996): 121-130. <http://eudml.org/doc/270028>.
@article{BogdanPrzeradzki1996,
abstract = {The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.},
author = {Bogdan Przeradzki},
journal = {Annales Polonici Mathematici},
keywords = {multiple solution; resonance; functional-differential equation; nonlinear equations; semilinear equations at resonance; degree theory; boundary value problems},
language = {eng},
number = {2},
pages = {121-130},
title = {A topological version of the Ambrosetti-Prodi theorem},
url = {http://eudml.org/doc/270028},
volume = {64},
year = {1996},
}
TY - JOUR
AU - Bogdan Przeradzki
TI - A topological version of the Ambrosetti-Prodi theorem
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 2
SP - 121
EP - 130
AB - The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.
LA - eng
KW - multiple solution; resonance; functional-differential equation; nonlinear equations; semilinear equations at resonance; degree theory; boundary value problems
UR - http://eudml.org/doc/270028
ER -
References
top- [1] H. Amann and P. Hess, A multiplicity result for a class of elliptic boundary value problems, Proc. Roy. Soc. Edinburgh 84A (1979), 145-151. Zbl0416.35029
- [2] A. Ambrosetti and G. Prodi, On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. Pura Appl. 93 (1973), 231-247. Zbl0288.35020
- [3] C. Fabry, J. Mawhin and M. Nkashama, A multiplicity result for periodic solutions of forced nonlinear second order differential equations, Bull. London Math. Soc. 18 (1986), 173-180. Zbl0586.34038
- [4] A. C. Lazer and P. J. McKenna, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl. 84 (1981), 282-284. Zbl0496.35039
- [5] A. C. Lazer and P. J. McKenna, On a conjecture related to the number of solutions of a nonlinear Dirichlet problem, Proc. Roy. Soc. Edinburgh 95A (1983), 275-283. Zbl0533.35037
- [6] J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Regional Conf. Ser. in Math. 40, Amer. Math. Soc., Providence, R.I., 1977.
- [7] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon Math. 53 (1991), 35-43. Zbl0746.47043
- [8] B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl. 180 (1993), 553-565. Zbl0807.34029
- [9] B. Przeradzki, Nonlinear boundary value problems at resonance for differential equations in Banach spaces, Math. Slovaca, to appear. Zbl0836.34065
- [10] B. Przeradzki, Three methods for the study of semilinear equations at resonance, Colloq. Math. 66 (1993), 109-129. Zbl0828.47054
- [11] B. Ruf, Multiplicity results for nonlinear elliptic equations, in: Proc. of the Spring School, Litomyšl, 1986, Teubner-Texte zur Math. 93, 1986, 109-138. Zbl0633.35027
- [12] S. Solimini, Multiplicity results for a nonlinear Dirichlet problem, Proc. Roy. Soc. Edinburgh 96A (1984), 331-336. Zbl0557.35052
NotesEmbed ?
topYou 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.