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 Vitali's convergence theorem. (C) 2003 Elsevier Ltd. All rights reserved.
existence singular higher-order differential equation (n,p) boundary conditions lidstone boundary conditions regularization topological degree vitali's theorem