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