On boundary value problems for third-order functional differential equations (Q1585015)

The existence of at least two solutions is proved for the functional-differential equation \[ (g(x''(t)))'= (Fx)(t), \] satisfying the functional boundary conditions \[ \alpha(x)= 0,\quad \|x'\|= H(x),\quad \beta(x'')= 0. \] The method relies, besides another, on a topological transversality method of A. Granas et al. An illustrating example is supplied.