Czechoslovak Mathematical Journal

, Volume 56, Issue 4, pp 1243–1263

Nodal solutions for a second-order m-point boundary value problem

  • Ruyun Ma
Article

DOI: 10.1007/s10587-006-0092-7

Cite this article as:
Ma, R. Czech Math J (2006) 56: 1243. doi:10.1007/s10587-006-0092-7

Abstract

We study the existence of nodal solutions of the m-point boundary value problem
$$\begin{gathered} u'' + f(u) = 0,0 < t < 1, \hfill \\ u'(0) = 0,u(1) = \sum\limits_{i = 1}^{m - 2} {\alpha _i u(\eta i)} \hfill \\ \end{gathered} $$
where ηi ∈ ℚ (i = 1, 2, ..., m − 2) with 0 < η1 < η2 < ... < ηm−2 < 1, and αi ∈ ℝ (i = 1, 2, ..., m − 2) with αi > 0 and \(\sum\nolimits_{i = 1}^{m - 2} {\alpha _i } \) < 1. We give conditions on the ratio f(s)/s at infinity and zero that guarantee the existence of nodal solutions. The proofs of the main results are based on bifurcation techniques.

Keywords

multiplicity resultseigenvaluesbifurcation methodsnodal zerosmulti-point boundary value problems

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2006

Authors and Affiliations

  • Ruyun Ma
    • 1
  1. 1.Department of MathematicsNorthwest Normal UniversityLanzhouP.R. China