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Radial Solutions for a Dirichlet Problem in a Ball

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Djairo G. de Figueiredo - Selected Papers

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Abstract

The Ambrosetti-Prodi boundary value problem with an asymptotically linear nonlinearity is considered. Under general conditions on the nonlinearity it is shown that there exist positive and negative solutions. In the case when the domain is a ball in Rn and the nonlinearity “crosses” the first n eigenvalues, corresponding to radial eigenfunctions, it is proved that there are at least n + 1 radial solution.

D. G. Costa, Partially supported by CNPq/Brazil.

D. G. De Figueiredo, Guggenheim Fellow, 1983.

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References

  1. A. AMBROSETTI, Elliptic equations with jumping nonlinearities, to appear.

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  2. D. G. DE FIGUEIREDO, “On the Superlinear Ambrosetti-Prodi Problem,” MRC Tech. Rep., No. 2522, May 1983.

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  3. A. C. LAZER AND P. J. MCKENNA, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl. 84 (1981), 282-294.

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  4. A. C. LAZER AND P. J. MCKENNA, On a conjecture related to the number of solutions of a nonlinear Dirichlet problem, to appear.

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  5. S. SOLIMINI, Existence of a third solution for a class of b.v.p. with jumping nonlinearities, Nonlinear Anal. TMA 7 (8) (1983), 917-927.

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Acknowledgments

The present research was done when both authors were visiting the Mathematics Research Center of the University of Wisconsin, whose hospitality they gratefully acknowledge.

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Authors and Affiliations

  1. Departamento de Matematica, Universidade de Brasilia, Caixa Postal 15301, Brasilia, DF, 70910, Brazil

    D. G. Costa & D. G. De Figueiredo

Authors
  1. D. G. Costa
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  2. D. G. De Figueiredo
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Correspondence to D. G. Costa .

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Editors and Affiliations

  1. University of Nevada Las Vegas Dept. Mathematical Sciences, Las Vegas, Nevada, USA

    David G. Costa

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© 1985 Academic Press, Inc.

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Costa, D.G., De Figueiredo, D.G. (1985). Radial Solutions for a Dirichlet Problem in a Ball. In: Costa, D. (eds) Djairo G. de Figueiredo - Selected Papers. Springer, Cham. https://doi.org/10.1007/978-3-319-02856-9_14

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