Nonlinear perturbations of differential operators with nontrivial kernel and applications to third-order periodic boundary value problems. (English) Zbl 0695.47044

Summary: This deals with the solvability of the nonlinear operator equations in normed spaces \({\mathcal L}x=EGx+f\), where \({\mathcal L}\) 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.


47E05 General theory of ordinary differential operators
47F05 General theory of partial differential operators
34C25 Periodic solutions to ordinary differential equations
47A53 (Semi-) Fredholm operators; index theories
Full Text: DOI


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