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A note on resonance problems with nonlinearity bounded in one direction

Published online by Cambridge University Press:  17 April 2009

To Fu Ma  and
Luís Sanchez
To Fu Ma
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, 87020–900 Maringá-PR, Brazil, e-mail: [email protected]
Luís Sanchez
Affiliation:
Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Rua Ernesto de Vasconcelos, Bloco Cl, 1700 Lisboa, Portugal, e-mail: [email protected]
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Abstract

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We prove the existence of a solution for a semilinear boundary value problem at resonance in the first eigenvalue. The nonlinearity is assumed to be bounded below or above; no further growth restrictions are assumed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 183 - 188
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Ahmad, S., ‘A resonance problem in which the nonlinearity may grow linearly’, Proc. Amer. Math. Soc. 92 (1984), 381–384.CrossRefGoogle Scholar
[2]Berestycki, H. and de Figueiredo, D.G., ‘Double resonance in semilinear elliptic problems’, Comm. Partial Differential Equations 6 (1981), 91–120.CrossRefGoogle Scholar
[3]Chiappinelli, R., Mawhin, J. and Nugari, R., ‘Bifurcation from infinity and multiple solutions for some Dirichlet problems with unbounded nonlinearities’, Nonlinear Anal. 18 (1992), 1099–1112.CrossRefGoogle Scholar
[4]Chiappinelli, R. and De Figueiredo, D.G., ‘Bifurcation from infinity and multiple solutions for an elliptic system’, Differential Integral Equations 6 (1993), 757–771.CrossRefGoogle Scholar
[5]Ha, Chung-Wei and Song, Wen-Bing, ‘On a resonance problem with nonlinearities of arbitrary polynomial growth’, Bull. Austr. Math. Soc. 48 (1993), 435–440.CrossRefGoogle Scholar
[6]Gaines, R.E. and Mawhin, J., Coincidence degree and nonlinear differential equations, Lecture Notes in Math. 558 (Springer-Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[7]Iannacci, R. and Nkashama, M.N., ‘Nonlinear boundary value problems at resonance’, Nonlinear. Anal. 11 (1987), 455–473.CrossRefGoogle Scholar
[8]Landesman, E.M. and Lazer, A.C., ‘Nonlinear perturbations of a linear elliptic boundary value problem at resonance’, J. Math. Mech. 19 (1970), 609–623.Google Scholar