We revive the study of the symmetric three-term recurrence equations. Our main result shows that these equations have a natural symplectic structure, that is, every symmetric three-term recurrence equation is a special discrete symplectic system. The assumptions on the coefficients in this paper are weaker and more natural than those in the current literature. In addition, our result implies th...

The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the ...

The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseu...

The Estabrook-Wahlquist method for establishing the integrability of partial diierential equations is extended to semi-discrete (lattice) systems. If successful, the method construct the linear eigenvalue problem associated with the equation.

The boundary value problem for ordinary differential equations is considered and a general theory for difference approximation is developed. In particular, the influence of extra boundary conditions is investigated and the eigenvalue problem is considered in detail.

The existence and multiplicity of solutions for a class non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise solution behaviors as result effect. Comparisons made results here those problem absence term under same prescribed conditions to highlight effect non-locality on behaviors. Ou...

In this paper, we prove the optimal upper bound ?n?m?(nm)2 of vibrating string?y?=??(x)y, with Dirichlet boundary conditions for single-well densities. The proof is based on inequality ?n(?)?m(?)??n(L)?m(L), L must be a stepfunction. We also same result Sturm-Liouville problems.