In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for ...In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.展开更多
Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutio...In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, ι, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).展开更多
In this paper we study the Oscillatory behaviour of the second order delay differenceequation.（1）△（r<sub>n</sub>△A<sub>n</sub>）+P<sub>n</sub>A<sub>n-k</sub>=0,n=n&...In this paper we study the Oscillatory behaviour of the second order delay differenceequation.（1）△（r<sub>n</sub>△A<sub>n</sub>）+P<sub>n</sub>A<sub>n-k</sub>=0,n=n<sub>0</sub>,n<sub>0</sub>+1……where{P<sub>n</sub>}（?）is a nonnegative Sequenceof real number,（?）is a positive sequence of real number with sum from n=n<sub>0</sub> to +∞（1/r<sub>n</sub>）=+∞,K is a positive integer and △A<sub>n</sub>=A<sub>n+1</sub>-A<sub>n</sub> we prove that each one of following conditions.imples that al solutions of Eq（1）oscillate,where R<sub>n</sub>=sum from i=n<sub>0</sub> to n（1/r<sub>i</sub>展开更多
Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be ...Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.展开更多
Comparison and oscillation theorems which relate to the oscillatory behaviors among the members of a class of 'advanced type' difference equations are derived. Among others, these theorems show that oscillati...Comparison and oscillation theorems which relate to the oscillatory behaviors among the members of a class of 'advanced type' difference equations are derived. Among others, these theorems show that oscillation criteria for the standard second order linear difference equation can be applied to these equations. Oscillation criterion for a nonlinear advanced type difference equation is also derived as an application.AMS 1991 Subject classification: 39A10展开更多
文摘In this paper, oscillatory properties of all solutions for neutral type impulsive hyperbolic equations with several delays under the Robin boundary condition are investigated and several new sufficient conditions for oscillation are presented.
文摘Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).
文摘In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, ι, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).
文摘In this paper we study the Oscillatory behaviour of the second order delay differenceequation.（1）△（r<sub>n</sub>△A<sub>n</sub>）+P<sub>n</sub>A<sub>n-k</sub>=0,n=n<sub>0</sub>,n<sub>0</sub>+1……where{P<sub>n</sub>}（?）is a nonnegative Sequenceof real number,（?）is a positive sequence of real number with sum from n=n<sub>0</sub> to +∞（1/r<sub>n</sub>）=+∞,K is a positive integer and △A<sub>n</sub>=A<sub>n+1</sub>-A<sub>n</sub> we prove that each one of following conditions.imples that al solutions of Eq（1）oscillate,where R<sub>n</sub>=sum from i=n<sub>0</sub> to n（1/r<sub>i</sub>
文摘Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.
文摘Comparison and oscillation theorems which relate to the oscillatory behaviors among the members of a class of 'advanced type' difference equations are derived. Among others, these theorems show that oscillation criteria for the standard second order linear difference equation can be applied to these equations. Oscillation criterion for a nonlinear advanced type difference equation is also derived as an application.AMS 1991 Subject classification: 39A10
