A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems

Autor: Ghasem Alizadeh Afrouzi, Shapour Heidarkhani
Jazyk: angličtina
Rok vydání: 2006
Předmět:
Zdroj: Electronic Journal of Differential Equations, Vol 2006, Iss 121, Pp 1-10 (2006)
Druh dokumentu: article
ISSN: 1072-6691
Popis: 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 $$displaylines{ -u''(x)+m(x)u(x) =lambda f(x,u(x)),quad xin (a,b),cr u(a)=u(b)=0, }$$ where $lambda>0$, $f:[a,b]imes mathbb{R}o mathbb{R}$ is a continuous function which changes sign on $[a,b]imes mathbb{R}$ and $m(x)in C([a,b])$ is a positive function.
Databáze: Directory of Open Access Journals