Nonlinear Perturbations of Differential Operators with Nontrivial Kernel and Applications to Third Order Periodic Boundary Value Problems.

摘要

This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs. (Atomindex citation 19:059898)