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 |
| Externí odkaz: |
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