Sadyrbaev, F. Multiplicity in parameter-dependent problems for ordinary differential equations. (English) Zbl 1193.34030 Math. Model. Anal. 14, No. 4, 503-514 (2009). The author presents some properties of the spectrum in connection with the number of solutions to the boundary value problems \[ x''+\lambda f(x)=0,\,\,\,x\in (0,1),\,\,\,x(0)=0,\,\,x(1)=0, \] where \(f\) is a continuously differentiable function and \(\lambda\) is a parameter, and \[ x''=-\lambda f(x^+)+\mu g(x^-),\,\,\,x\in (0,1),\,\,\,x(0)=0,\,\,x(1)=0, \] where \(x^+=\max\{x,0\}\), \(x^-=\max\{-x,0\}\), \(\lambda,\,\mu\) are nonnegative parameters and \(f,\,g\) are positive continuously differentiable functions defined on \(\mathbb{R}^+=[0,\infty)\). Reviewer: Rodica Luca Tudorache (Iaşi) Cited in 1 Document MSC: 34B09 Boundary eigenvalue problems for ordinary differential equations 34B08 Parameter dependent boundary value problems for ordinary differential equations 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators Keywords:nonlinear boundary value problems; Fucik spectra; multiplicity of solutions; solution curves; bifurcation diagrams PDFBibTeX XMLCite \textit{F. Sadyrbaev}, Math. Model. Anal. 14, No. 4, 503--514 (2009; Zbl 1193.34030) Full Text: DOI