In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)...In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.展开更多
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
In this paper,some sufficient conditions are obtained for the oscillation for solutions of systems of highd order partial differential equations of neutral type.
This review considers unexpected destructive disasters involving fluid power plants, such as nuclear electric power plants and fluid power plants. It specifically addresses the possibility of fluid vibration induced i...This review considers unexpected destructive disasters involving fluid power plants, such as nuclear electric power plants and fluid power plants. It specifically addresses the possibility of fluid vibration induced in a pipeline network of such a plant. The authors investigate the flow oscillation induced within a T-junction for laminar steady flow at a Reynolds number less than 10<sup>3</sup> and clarify that there is a periodic fluid oscillation with a constant Strouhal number independent of several flow conditions. Generally, a nuclear electric power plant is constructed using straight pipes, elbows, and T-junctions. Indeed, a T-Junction is a basic fluid element of a pipeline network. The flow in a fluid power plant is turbulent. There are peculiar flow phenomena that occur at high Reynolds numbers, which are also seen in other flow situations;e.g., Kaman vortices are observed around a circular cylinder in low Reynolds numbers, around structures like bridges and downstream of islands in oceans. Although the flow situation of a T-junction and elbow in a fluid power plant, such as the fluid suddenly changing its flow direction is turbulent flow, the authors mention the possibility of the fluid-induced vibration of a pipeline network.展开更多
Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were con...Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.展开更多
In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j...In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.展开更多
Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical doma...Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical domain are obtained.展开更多
In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.
Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn...The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.展开更多
Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous ...Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.展开更多
Our aim in this paper is to obtain a necessary and sufficient condition characterized by coefficients and delays under which every solution of higher-order neutral equation will be oscillating, where p ≠ 0, τ > ...Our aim in this paper is to obtain a necessary and sufficient condition characterized by coefficients and delays under which every solution of higher-order neutral equation will be oscillating, where p ≠ 0, τ > 0, σ> 0 and q are all constants.展开更多
This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having diffe...This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having differentcharacters.展开更多
In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions fo...In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.展开更多
The objective of this paper is to study the oscillatory and asymptotic properties of the general mixed type third order neutral difference equation of the form △（aαn△2（xn＋ bnxn-τ1＋ cnxn＋τ2）） ＋ qnx^a n＋1...The objective of this paper is to study the oscillatory and asymptotic properties of the general mixed type third order neutral difference equation of the form △（aαn△2（xn＋ bnxn-τ1＋ cnxn＋τ2）） ＋ qnx^a n＋1-σ＋ pnx^βn＋1＋=σ2 0,where {an}, {bn}, {cn}, {qn} and {pn} are positive real sequences, both α and β are ratios of odd positive integers, τ1, τ2, σ1 and σ2 are positive integers. We establish some sufficient conditions which ensure all solutions are either oscillatory or converge to zero.展开更多
文摘In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.
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In this paper,some sufficient conditions are obtained for the oscillation for solutions of systems of highd order partial differential equations of neutral type.
文摘This review considers unexpected destructive disasters involving fluid power plants, such as nuclear electric power plants and fluid power plants. It specifically addresses the possibility of fluid vibration induced in a pipeline network of such a plant. The authors investigate the flow oscillation induced within a T-junction for laminar steady flow at a Reynolds number less than 10<sup>3</sup> and clarify that there is a periodic fluid oscillation with a constant Strouhal number independent of several flow conditions. Generally, a nuclear electric power plant is constructed using straight pipes, elbows, and T-junctions. Indeed, a T-Junction is a basic fluid element of a pipeline network. The flow in a fluid power plant is turbulent. There are peculiar flow phenomena that occur at high Reynolds numbers, which are also seen in other flow situations;e.g., Kaman vortices are observed around a circular cylinder in low Reynolds numbers, around structures like bridges and downstream of islands in oceans. Although the flow situation of a T-junction and elbow in a fluid power plant, such as the fluid suddenly changing its flow direction is turbulent flow, the authors mention the possibility of the fluid-induced vibration of a pipeline network.
文摘Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
基金Supported by the National Natural Science Foundation of China
文摘In this paper. we deal with the oscillatory behavior of solutions of the neutral partial differential equation of the form /t[p(t)/t(u(x.t)+sun from i=1 to t pi(t)u(x,t-ti))]+q(x,t)u(x,t)+sun form j=1 to m qj(x,t)f_j(u(x,σ_j(t))) =a(t)△u(x,t)+sun form k=1 to n ak(t)△u(x,pk(t)), (x,t)∈Ω×R_+≡G where △ is the Laplacian in Euclidean N-space R^N, R_+=(0, ∞) and Ω is a bounded domain in R^N with a piecewise smooth boundary Ω.
文摘Neutral hyperbolic differential equations with continuous distributed devia-ting arguments are studied, and sufficient conditions for each solution of the boundary value problem to be oscillatory in a cylindrical domain are obtained.
基金Project supported by Natural Science Foundation of Educational Department of Shandong Province(03P51)(J04A60).
文摘In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.
文摘Sufficient conditions are obtained for the oscillation of the solutions to nonlinear parabolic differential equations of neutral type in the form of where Ω is a bounded domain in Rn with a piecewise smooth boundary.
文摘The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.
文摘Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.
文摘Our aim in this paper is to obtain a necessary and sufficient condition characterized by coefficients and delays under which every solution of higher-order neutral equation will be oscillating, where p ≠ 0, τ > 0, σ> 0 and q are all constants.
文摘This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having differentcharacters.
基金Supported by the National Natural Science Foundation of China(10471086).
文摘In this paper, we study the oscillation of solutions to the systems of impulsive neutral delay parabolic partial differential equations. Under two different boundary conditions, we obtain some sufficient conditions for oscillation of all solutions to the systems.
基金Supported by Science Research Foundation of Guangxi Education Board under grant YB2014117
文摘The objective of this paper is to study the oscillatory and asymptotic properties of the general mixed type third order neutral difference equation of the form △（aαn△2（xn＋ bnxn-τ1＋ cnxn＋τ2）） ＋ qnx^a n＋1-σ＋ pnx^βn＋1＋=σ2 0,where {an}, {bn}, {cn}, {qn} and {pn} are positive real sequences, both α and β are ratios of odd positive integers, τ1, τ2, σ1 and σ2 are positive integers. We establish some sufficient conditions which ensure all solutions are either oscillatory or converge to zero.
