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ON AN OPEN QUESTION OF RICCERI CONCERNING A NEUMANN PROBLEM

Published online by Cambridge University Press:  09 August 2007

FRANCESCA FARACI  and
ALEXANDRU KRISTÁLY
FRANCESCA FARACI
Affiliation:
University of Catania, Department of Mathematics, 95125 Catania, Italy email: [email protected]
ALEXANDRU KRISTÁLY
Affiliation:
University of Babeş-Bolyai, Department of Economics, 400591 Cluj-Napoca, Romania email: [email protected]
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Abstract

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In this paper we solve partially an open problem raised by B. Ricceri (Bull. London Math. Soc.33 (2001), 331–340). Infinitely many solutions for a Neumann problem are obtained through a direct variational approach where the nonlinearity has an oscillatory behaviour at infinity.

Keywords

35J2035J25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 2 , May 2007 , pp. 189 - 195
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1. Anello, G. and Cordaro, G., Infinitely many positive solutions for the Neumann problem involving the p-Laplacian, Colloq. Math. 97 (2003), 221–231.CrossRefGoogle Scholar
2. Marcus, M. and Mizel, V., Every superposition operator mapping one Sobolev space into another is continuous, J. Functional Analysis 33 (1979), 217–229.CrossRefGoogle Scholar
3. Ricceri, B., A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401–410.CrossRefGoogle Scholar
4. Ricceri, B., Infinitely many solutions of the Neumann problem for elliptic equations involving the p-Laplacian, Bull. London Math. Soc. 33 (2001), 331–340.CrossRefGoogle Scholar
5. Ricceri, B., Some research perspectives in nonlinear functional analysis, International Conference on Nonlinear Operators, Differential Equations and Applications (Cluj-Napoca, 2001) in Semin. Fixed Point Theory Cluj-Napoca 3 (2002), 99–109.Google Scholar
6. Saint, J. Raymond, On the multiplicity of solutions of the equation −Δu=λf(u), J. Differential Equations 180 (2002), 65–88.CrossRefGoogle Scholar