On a variational statement of a nonlocal boundary value problem for a fourth-order ordinary differential equation
The paper deals with the existence of solutions to a differential equation of the form \[ (k_1(x)u''(x))''-(k_2(x)u'(x))'+k_3(x)u(x)=f(x) \] satisfying the boundary conditions \[ u(-a)=u'(-a)=u'(0)=0\text{ and }\int_{-\xi}^0k_2(x)u'(x)dx-k_1(0)u''(0))+k_1(-\xi)u''(-\xi)=0. \] The authors formulate a minimizing functional defined on an appropriate Hilbert space and then they show that the minimum of the functional is a solution of the original boundary value problem.
fourth-order ordinary differential equations
scientific article; zbMATH DE number 5611153
scientific article