## Taiwanese Journal of Mathematics

### Existence of Three Solutions for a Doubly Eigenvalue Fourth-order Boundary Value Problem

#### Abstract

In this paper we consider the existence of at least three solutions for the Dirichlet problem $$\left\{\begin{array}{ll} u^{i\upsilon} + \alpha u'' + \beta u = \lambda f(x,u) + \mu g(x,u), \hspace{1cm} x \in (0,1) \\ u(0) = u(1) = 0, \\ u''(0) = u''(1) = 0 \end{array}\right.$$ where $\alpha,\ \beta$ are real constants, $f,g: [0,1] \times R \to R$ are $L^{2}$-Carathéodory functions and $\lambda,\mu \gt 0$. The approach is based on variational methods and critical points.

#### Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 201-210.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406170

Digital Object Identifier
doi:10.11650/twjm/1500406170

Mathematical Reviews number (MathSciNet)
MR2780280

Subjects
Primary: 34B15: Nonlinear boundary value problems

#### Citation

Afrouz, G. A.; Heidarkhani, S.; O’Regan, Donal. Existence of Three Solutions for a Doubly Eigenvalue Fourth-order Boundary Value Problem. Taiwanese J. Math. 15 (2011), no. 1, 201--210. doi:10.11650/twjm/1500406170. https://projecteuclid.org/euclid.twjm/1500406170