In this paper, generalized boundary value problems for nonlinear fractional Langevin equations is studied. Some new existence results of solutions in the balls with different radius are obtained when the nonlinear term satisfies nonlinear Lipschitz and linear growth conditions. Finally, two examples are given to illustrate the results.
It is shown that for a given system of linearly independent linear continuous functionals , , the set of all -th order linear differential equations such that the Green function for the corresponding generalized boundary value problem (BVP for short) exists is open and dense in the space of all -th order linear differential equations. Then the generic properties of the set of all solutions to nonlinear BVP-s are investigated in the case when the nonlinearity in the differential equation has...
Boundary value problems for generalized linear differential equations and the corresponding controllability problems are dealt with. The adjoint problems are introduced in such a way that the usual duality theorems are valid. As a special case the interface boundary value problems are included. In contrast to the earlier papers by the author the right-hand side of the generalized differential equations as well as the solutions of this equation can be in general regulated functions (not necessarily...
The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is , i=1,..., r, where denote some homogeneous polynomials of degrees constructed from functional variables and their derivatives. It is assumed that . The problem...
In the paper a comparison theory of Sturm-Picone type is developed for the pair of nonlinear second-order ordinary differential equations first of which is the quasilinear differential equation with an oscillatory forcing term and the second is the so-called half-linear differential equation. Use is made of a new nonlinear version of the Picone’s formula.