A topological version of the Ambrosetti-Prodi theorem

• Autorzy: Bogdan Przeradzki
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multiple solution; resonance; functional-differential equation

Kategorie tematyczne

• 34K10: Boundary value problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 2
• Strony: 121-130

Daty

wydano

1996

otrzymano

1995-03-20

Twórcy

autor

Bogdan Przeradzki

• Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [8] B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl. 180 (1993), 553-565.
• [9] B. Przeradzki, Nonlinear boundary value problems at resonance for differential equations in Banach spaces, Math. Slovaca, to appear.
• [10] B. Przeradzki, Three methods for the study of semilinear equations at resonance, Colloq. Math. 66 (1993), 109-129.
• [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.
• [12] S. Solimini, Multiplicity results for a nonlinear Dirichlet problem, Proc. Roy. Soc. Edinburgh 96A (1984), 331-336.