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A note on a problem by Ricceri on the Ambrosetti-Rabinowitz condition


Author: Giovanni Anello
Journal: Proc. Amer. Math. Soc. 135 (2007), 1875-1879
MSC (2000): Primary 47J30
Published electronically: January 8, 2007
MathSciNet review: 2286099
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Abstract: In this note we give an answer to Ricceri's open problem involving the Ambrosetti-Rabinowitz superlinear condition.


References [Enhancements On Off] (What's this?)

  • 1. Antonio Ambrosetti and Paul H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis 14 (1973), 349–381. MR 0370183
  • 2. Biagio Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), no. 1-2, 401–410. Fixed point theory with applications in nonlinear analysis. MR 1735837, 10.1016/S0377-0427(99)00269-1
  • 3. Biagio Ricceri, Some research perspectives in nonlinear functional analysis, Semin. Fixed Point Theory Cluj-Napoca 3 (2002), 99–109. International Conference on Nonlinear Operators, Differential Equations and Applications (Cluj-Napoca, 2001). MR 1929750
  • 4. Biagio Ricceri, On a classical existence theorem for nonlinear elliptic equations, Constructive, experimental, and nonlinear analysis (Limoges, 1999), CMS Conf. Proc., vol. 27, Amer. Math. Soc., Providence, RI, 2000, pp. 275–278. MR 1777629

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Additional Information

Giovanni Anello
Affiliation: Department of Mathematics, University of Messina, 98166 S. Agata, Messina, Italy
Email: anello@dipmat.unime.it

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08674-1
Received by editor(s): December 5, 2005
Received by editor(s) in revised form: February 19, 2006
Published electronically: January 8, 2007
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.