Abstract
Using a recent variational principle of B. Ricceri, we present some results of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian.
Because of surprising coicidence of names within the same Department, we have to point out the author was born on August 4, 1968.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. Cammaroto and A. Chinnì. Infinitely many solutions for a two points boundary value problem. Far East Journal of Mathematical Sciences, 11, n. 1:41–51, 2003.
P. Korman and Y. LI. Infinitely many solutions at a resonance. Nonlinear Differential Equations, pages 105–111, 2000.
G.B. Li and H.S. Zhou. Multiple solutions to p-Laplacian problems with asymptotic nonlinearity as u p−1 at infinity. J. London Math. Soc., 65, n. 2:123–138, 2002.
P. Omari and F. Zanolin. Infinitely many solutions of a quasilinear elliptic problem with an oscillatory potential. Commun. in Partial Differential Equations, 21:721–733, 1996.
P. Omari and F. Zanolin. An elliptic problem with arbitrarily small positive solutions. Nonlinear Differential Equations, Electron. J. Diff. Eqns., Conf. 05: 301–308, 2000.
B. Ricceri. A general variational principle and some of its applications. J. Comput. Appl. Math., 113:401–410, 2000.
J. Saint Raymond. On the multiplicity of the solutions of the equation − Δu = λf(u). J. Differential Equations, 180: 65–88, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Cammaroto, F., Chinnì, A., Di Bella, B. (2005). Infinitely Many Solutions for the Dirichlet Problem Via a Variational Principle of Ricceri. In: Giannessi, F., Maugeri, A. (eds) Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol 79. Springer, Boston, MA. https://doi.org/10.1007/0-387-24276-7_16
Download citation
DOI: https://doi.org/10.1007/0-387-24276-7_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24209-5
Online ISBN: 978-0-387-24276-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)