Acta Mathematica Sinica, English Series

, Volume 24, Issue 1, pp 27–34

Nodal solutions for a nonlinear fourth-order eigenvalue problem


DOI: 10.1007/s10114-007-1009-6

Cite this article as:
Ma, R.Y. & Thompson, B. Acta. Math. Sin.-English Ser. (2008) 24: 27. doi:10.1007/s10114-007-1009-6


We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem
$$ \begin{gathered} y'''' = \lambda a(x)f(y),0 < x < 1, \hfill \\ y(0) = y(1) = y''(0) = y'' = (1) = 0, \hfill \\ \end{gathered} $$
where λ is a positive parameter, aC([0, 1], (0, ∞)), fC (ℝ, ℝ) satisfies f(u)u > 0 for all u ≠ 0. We give conditions on the ratio f(s)/s, at infinity and zero, that guarantee the existence of nodal solutions. The proof of our main results is based upon bifurcation techniques.


multiplicity resultseigenvaluesbifurcation methodsnodal zeros

MR(2000) Subject Classification


Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsNorthwest Normal UniversityLanzhouP. R. China
  2. 2.Department of Mathematicsthe University of QueenslandBrisbaneAustralia