# A topological version of the Ambrosetti-Prodi theorem

Annales Polonici Mathematici (1996)

- Volume: 64, Issue: 2, page 121-130
- ISSN: 0066-2216

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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

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