Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 41, pp. 1-14.

Title: Existence of trivial and nontrivial solutions of a fourth-order 
       ordinary differential equation
       
Authors: Tihomir Gyulov (Univ. of Rousse, Bulgaria)
   Stepan Tersian (Univ. of Rousse, Bulgaria)

Abstract: 
We study the multiplicity of nontrivial solutions for a
 semilinear fourth-order ordinary differential equation arising in
 spatial patterns for bistable systems. In the proof of our results,
 we use minimization theorems and Brezis-Nirenberg's linking theorem.
 We obtain also estimates on the minimizers of the
 corresponding functionals.
  
Submitted January 5, 2004. Published March 23, 2004.
Math Subject Classifications: 34B15, 34C25, 35K35.
Key Words: Fourth-order ordinary differential equation;
           variational method; Brezis-Nirenberg's theorem.