โ Scribed by Kenneth R. Ludwig; Paul R. Renne
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this paper we study the process of Riemann and Lebesgue integration on time scales. The relationship of the Riemann and Lebesgue integrals is considered and a criterion for Riemann integrability is established.
Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is con
Linear and nonlinear Hamiltonian systems are studied on time scales . We unify symplectic flow properties of discrete and continuous Hamiltonian systems. A chain rule which unifies discrete and continuous settings is presented for our so-called alpha derivatives on generalized time scales. This chai
We consider the structure of the solution set of a nonlinear Sturm-Liouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, an
Eventual disconjugacy of the time scale differential equation yAA(t) + pl(t)yA(t) + p2(t)y(t) = 0 is established. These nonoscillation theorems are achieved by imposing integrability conditions on P],P2.