Two-point higher-order BVPs with singularities in phase variables

The existence of solutions for singular higher-order differential equations with the Lidstone or the (n,p) boundary conditions is proved. The right-hand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities. Proofs are based on the method of a priori estimates, the degree theory arguments and on Vitaliʹs convergence theorem.