The state linear system (A(t), B(t), C(t)) of (1)-(2) is called a nonautonomous Sturm-Liouville system if A(t) is the negative of a nonautonomous Sturm-Liouville operator of form (54).
Corollary 15 also concludes that any nonautonomous Sturm-Liouville system is the nonautonomous Riesz-spectral system.
Mukhtarov, "Generalized Fourier series as Green's function expansion for multi-interval
Sturm-Liouville systems," Mediterranean Journal of Mathematics, vol.
The topics include nontrivial solutions of
Sturm-Liouville systems, infinitely many solutions of multi-point problems, anti-periodic solutions for impulsive problems, a Kirchhoff-type problem involving two parameters, and homoclinic solutions for difference equations.
Coverage encompasses special functions in science and engineering;
Sturm-Liouville systems and the factorization method; coordinates and tensors; continuous groups, Lie algebras, and group representations; complex analysis; the basics of fractional calculus; infinite series; integral transforms; variational analysis; integral equations; Green's functions; and path integrals.
The relationships between Fourier expansions in nonlinear systems with the orthonormal sets are obtained as characteristics functions of
Sturm-Liouville systems. The nonlinear stability is also studied.