Abstract
We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions $$\left\{ \begin{gathered} u^{(4)} (t) = f(t,u(t),u'(t),u''(t),u'''(t)),a.e.t \in [0,1], \hfill u(0) = a,u'(0) = b,u(1) = c,u''(1) = d, \hfill \end{gathered} \right. $$ where the nonlinear term f(t, u0, u1, u2, u3) is a strong Caratheodory function. By constructing suitable height functions of the nonlinear term f(t, u0, u1, u2, u3) on bounded sets and applying the Leray-Schauder fixed point theorem, we prove that the equation has a solution provided that the integration of some height function has an appropriate value.
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