Acta Mathematica Sinica, English Series

, Volume 24, Issue 1, pp 27–34

Nodal solutions for a nonlinear fourth-order eigenvalue problem

Authors

    • Department of MathematicsNorthwest Normal University
  • Bevan Thompson
    • Department of Mathematicsthe University of Queensland
Article

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

Abstract

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.

Keywords

multiplicity resultseigenvaluesbifurcation methodsnodal zeros

MR(2000) Subject Classification

34B15

Copyright information

© Springer-Verlag 2008