Countably many solutions of a fourth order boundary value problem - Nickolai Kosmatov (Electronic Journal of Qualitative Theory of Differential Equations, 2004)
We apply fixed point theorems to obtain sufficient conditions for existence of infinitely many solutions of a nonlinear fourth order boundary value problem $$\displaylines{ u^{(4)}(t) = a(t)f(u(t)), \quad 0 < t < 1, \cr u(0) = u(1) = u'(0) = u'(1) = 0, }$$ where $a(t)$ is $L^p$-integrable and $f$ satisfies certain growth conditions.