Yonghong Wu

Some physical structures for the (2+1) -dimensional Boussinesq water equation with positive and negative exponents

In this paper, a mathematical method is constructed to study two variants of the two-dimensional Boussinesq water equation with positive and negative exponents. In terms of travelling wave solutions, the partial differential equations are transformed to nonlinear ordinary differential equations. Exact solutions are then derived for various cases to describe the different physical structures such as compactons, solitons, solitary patterns and periodic solutions. The exponent of the wave function u and the ratio of the two coefficients a and b in the Boussinesq equation are shown to qualitatively determine the physical structures of the solutions.

Extremal solutions for p-Laplacian differential systems via iterative computation

Abstract In this paper, we study the extremal solutions of a fractional differential system involving the p -Laplacian operator and nonlocal boundary conditions. The conditions for the existence of the maximal and minimal solutions to the system are established. In addition, we also derive explicit formulae for the estimation of the lower and upper bounds of the extremal solutions, and establish a convergent iterative scheme for finding these solutions. We also give a special case in which the conditions for the existence of the extremal solutions can be easily verified.

The unique solution of boundary value problems for nonlinear second-order integral-differential equations of mixed type in Banach spaces

In this paper, a class of two-point boundary value problems for nonlinear second-order integral-differential equations of mixed type is investigated in a real Banach space without making any compactness type assumption; we establish conditions for the existence of a unique solution of the equation and develop an iterative formula for approximation of the solution and a formula for estimating the error of the iterative solution. The results we obtained generalize and improve various recent results.

Triple positive solutions of a boundary value problem for nonlinear singular second-order differential equations of mixed type with p-Laplacian

In this paper, we establish the existence of triple positive solutions of a two-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator. We also demonstrate that the results obtained can be applied to study certain higher order mixed boundary value problems. Finally, an example is given to demonstrate the use of the main results of this paper.

Higher even-order convergence and coupled solutions for second-order boundary value problems on time scales

In this paper, for a second-order boundary value problem on time scales, a method of generalized quasilinearization, under coupled upper and lower solutions, is discussed. An attempt for the method is to establish sufficient conditions for generating monotone iterative schemes whose elements converge rapidly to the unique solution of the given problem. Furthermore, the convergence is of order k(k>=2), which is even. Finally, two examples are provided to illustrate our results.

Criteria on boundedness in terms of two measures for discrete systems

A new concept of boundedness, which unifies various boundedness notions and leads to other notions connecting them, is defined in terms of two measures. An attempt for discrete systems tries to offer sufficient conditions for obtaining boundedness criteria for such concepts. The employing of vector Lyapunov functions and a new comparison principle covers several known results in usual boundedness theory and, therefore, the present framework provides an additional unification.