In this paper, we consider the characteristic initial–boundary value problem (IBVP) for the multi-dimensional Jin–Xin relaxation model in a half-space with arbitrary space dimension n52: As in the one-dimensional case (n 1⁄4 1; see (J. Differential Equations, 167 (2000), 388–437), our main interest is on the precise structural stability conditions on the relaxation system, particularly the form...

In this article, we study the existence of solutions to boundaryvalue problems for ordinary differential equations with two-point and integral boundary conditions. Existence and uniqueness results are obtained by using well known fixed point theorems. Some illustrative examples are also discussed.

This article concerns the existence of solutions to periodic boundaryvalue problems for second-order nonlinear differential equation involving fractional derivatives. Under certain linear growth condition of the nonlinearity, we obtain solutions, by using coincidence degree theory. An example illustrates our results.

In this article, we discuss the existence of solutions to boundaryvalue problems for a coupled system of fractional differential equations with p-Laplacian operator at resonance. We prove the existence of solutions when dim ker L ≥ 2, using the coincidence degree theory by Mawhin.

In this paper, we study a generalized Sturm-Liouville boundaryvalue problems with two positive parameters. By constructing a completely continuous operator and combining fixed point index theorem and some properties of the eigenvalues of linear operators, we obtain sufficient conditions for the existence of at least one positive solution.

Calculation schemes for numerical solution of elliptic boundary-value problems for Schrödinger-type equations based on Kantorovich method that reduces the initial problem to a set of boundary-value problems for a system of ordinary second-order differential equations are presented. The reduced boundaryvalue problems are discretized using the high-accuracy finite element method and implemented i...

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis nonlocal theory elasticity. The upper part spectrum with wavelength comparable to internal characteristic dimension a nanorod is examined. An equations in integral form Helmholtz kernel, incorporating both local and phases, used as constitutive one. original integro-differential equation reduc...

In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both q+(t) and q−(t) in addition to that of |q(t)|. The Green’s function for even order boundary-value problems plays a key role in our proofs. Also, using the Fredholm alternative theorem, we obtain a criterion for the existence and uniqueness of sol...

This paper investigates the discrete simulation of the solution of initial-boundaryvalue problems that typically arise in technical areas. Since many of them lead to unbounded and non-self-adjoint differential operators, we have to use a rather general theory as a mathematical basis. For the class of sectorial operators with a compact resolvent operator, the solution of initial-boundary-value p...