Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 121, pp. 1-10.
Title: A minimax inequality for a class of functionals and
applications to the existence of solutions for
two-point boundary-value problems
Authors: Ghasem Alizadeh Afrouzi (Mazandaran Univ., Babolsar, Iran)
Shapour Heidarkhani (Mazandaran Univ., Babolsar, Iran)
Abstract:
In this paper, we establish an equivalent statement to minimax
inequality for a special class of functionals. As an application,
we prove the existence of three solutions to the Dirichlet
problem
$$\displaylines{
-u''(x)+m(x)u(x) =\lambda f(x,u(x)),\quad x\in (a,b),\cr
u(a)=u(b)=0,
}$$
where $\lambda>0$, $f:[a,b]\times \mathbb{R}\to \mathbb{R}$ is a
continuous function which changes sign on $[a,b]\times \mathbb{R}$
and $m(x)\in C([a,b])$ is a positive function.
Submitted August 22, 2006. Published October 2, 2006.
Math Subject Classifications: 35J65.
Key Words: Minimax inequality; critical point; three solutions;
multiplicity results; Dirichlet problem.