Pei, Minghe; Chang, Sung Kag Solvability and dependence on a parameter of a fourth-order periodic boundary value problem. (English) Zbl 1331.34030 J. Appl. Math. Comput. 49, No. 1-2, 181-194 (2015). The authors investigate the solvability of the fourth-order boundary value problem \[ \begin{aligned} u^{(4)}(t)-&\rho u(t)+\lambda f(t, u(t))=0, \;\;0\leq t\leq 2\pi, \\ &u^{(i)}(0)=u^{(i)}(2\pi),\,\, i=0, 1, 2, 3,\end{aligned} \] where \(\rho\in (0, \frac 12)\) is a constant, \(f\in C([0,2\pi]\times \mathbb{R})\). The main tool is a fixed point theorem in cones. Uniqueness and dependence of solutions on the parameters are also investigated. Reviewer: Ruyun Ma (Lanzhou) MSC: 34B08 Parameter dependent boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:fourth-order equations; periodic boundary value problem; solvability; uniqueness; dependence of solutions PDFBibTeX XMLCite \textit{M. Pei} and \textit{S. K. Chang}, J. Appl. Math. Comput. 49, No. 1--2, 181--194 (2015; Zbl 1331.34030) Full Text: DOI References: [1] Amster, P., Mariani, M.C.: Oscillating solutions of a nonlinear fourth order ordinary differential equation. J. Math. Anal. Appl. 325, 1133-1141 (2007) · Zbl 1127.34007 [2] Bereanu, C.: Periodic solutions of some fourth-order nonlinear differential equations. 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