Geodesic
MINIMAX INEQUALITY FOR A SPECIAL CLASS OF FUNCTIONALS AND ITS APPLICATION TO EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET PROBLEM IN ONE-DIMENSIONAL CASE
AFROUZI, G. A.1 ; HEIDARKHANI, S.2 ; HOSSIENZADEH, H.3 ; YAZDANI, A.1
1 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
2 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
3 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 1, p. 1-11.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we establish an equivalent statement of minimax inequality for a special class of functionals. As an application, a result for the existence of three solutions to the Dirichlet problem
$ \begin{cases} -(|u'|^{p-2}u')' = \lambda f(x, u),\\ u(a) = u(b) = 0, \end{cases} $
where $f : [a; b] \times R\rightarrow R$ is a continuous function, $p > 1$ and $\lambda > 0$, is emphasized.
DOI : 10.22436/jnsa.003.01.01
Classification : 34A15, 5J20
Keywords: Minimax inequality, critical point, three solutions, multiplicity results, dirichlet problem.

AFROUZI, G. A. 1 ; HEIDARKHANI, S. 2 ; HOSSIENZADEH, H. 3 ; YAZDANI, A. 1

1 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
2 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
3 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran 
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AFROUZI, G. A.; HEIDARKHANI, S.; HOSSIENZADEH, H.; YAZDANI, A. MINIMAX INEQUALITY FOR A SPECIAL CLASS OF FUNCTIONALS AND ITS APPLICATION TO EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET PROBLEM IN ONE-DIMENSIONAL CASE. Journal of nonlinear sciences and its applications, Tome 3 (2010) no. 1, p. 1-11. doi : 10.22436/jnsa.003.01.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.003.01.01/

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