MINIMAX INEQUALITY FOR A SPECIAL CLASS OF FUNCTIONALS AND ITS APPLICATION TO EXISTENCE OF THREE SOLUTIONS FOR A DIRICHLET PROBLEM IN ONE-DIMENSIONAL CASE


Authors

G. A. AFROUZI - Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran. S. HEIDARKHANI - Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran. H. HOSSIENZADEH - Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran. A. YAZDANI - Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran.


Abstract

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.


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ISRP Style

G. A. AFROUZI, S. HEIDARKHANI, H. HOSSIENZADEH, A. YAZDANI, 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 Applications, 3 (2010), no. 1, 1--11

AMA Style

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. J. Nonlinear Sci. Appl. (2010); 3(1):1--11

Chicago/Turabian Style

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 Applications, 3, no. 1 (2010): 1--11


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