Solvability and dependence on a parameter of a fourth-order periodic boundary value problem
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.
scientific article; zbMATH DE number 6490706
scientific article