Qiru Wang

Oscillation of second-order nonlinear neutral dynamic equations on time scales

Abstract This paper is concerned with the oscillation of second-order nonlinear neutral dynamic equations of the form r ( t ) ( y ( t ) + p ( t ) y ( τ ( t ) ) ) Δ γ Δ + f ( t , y ( δ ( t ) ) ) = 0 , on a time scale T . By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation results which handle some cases not covered by known criteria.

Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales☆

Abstract This paper is concerned with cellular neural networks with time-varying delays in leakage terms on time scales. Some sufficient conditions on the existence, uniqueness, and global exponential stability of almost-periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results.

Approximate controllability of Riemann-Liouville fractional differential inclusions

In this paper, by using fractional calculus, multi-valued analysis, semigroup theory and the fixed-point technique, we study the approximate controllability for a class of Riemann-Liouville fractional differential inclusions. An example is given to illustrate the application of the abstract results.

Distribution of zeros of solutions of functional differential equations

Abstract By improving the bracketing techniques for a functional differential inequality in a previous paper [H.W. Wu, Y.T Xu, The distribution of zeros of solutions of neutral differential equations, Appl. Math. Comput. 156 (3) (2004) 665–677], we are able to derive sharper upper bounds on the distance between zeros of solutions of a class of neutral functional differential equations with delays, and hence improve many known bounds in the literature.

Oscillation criteria for second order nonlinear delay dynamic equations on time scales

By employing the generalized Riccati transformation, we establish some new oscillation criteria for second order delay dynamic equations on time scales. The obtained results essentially improve the well-know oscillation results for half-linear dynamic equations such as Kamenev-type and Philos-type oscillation criteria. Some interesting examples are given to illustrate the versatility of our results.

Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales

This paper is concerned with nth-order nonlinear dynamic equations on time scales of the form ( r ( t ) ? γ ( x Δ n - 1 ( t ) ) ) Δ + ? i = 0 k q i ( t ) ? α i ( x ( ? i ( t ) ) ) = 0 with n ? 2. By discussing the signs of ith-order derivatives of eventually positive solutions for i = 1 , ? , n - 1 , and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results extend many existing results in the literature.

Generalized Philos-type oscillation criteria for second order nonlinear neutral delay dynamic equations on time scales

Abstract By employing the generalized Riccati transformation w ( s ) and showing that [ H ( σ ( t ) , s ) w ( s ) ] Δ s ≤ 0 , we establish new Philos-type oscillation criteria for second order nonlinear dynamic equations on time scales. The obtained results essentially generalize and improve the well-known oscillation results for half-linear dynamic equations such as Philos-type and Kamenev-type oscillation criteria. We illustrate the versatility of our results by means of examples.

Cross-diffusion induced instability and pattern formation for a Holling type-II predator-prey model

This paper is devoted to studying a predator-prey model with Holling type-II functional response and cross-diffusion subject to Neumann boundary condition. Our main interest lies in the effects of cross-diffusion on stability and stationary patterns. More precisely, the presented results show that cross-diffusion can not only destabilize a uniform equilibrium which is stable for the kinetic and random diffusion reaction systems, but also create spatial patterns even when the random diffusion fails to do so. Furthermore, our results also reveal that, in this kind of ecological system, instability and stationary patterns can appear only when the predators rapidly move away from a large group of preys, regardless of the speed that the preys keep away from the predators.

Pseudo asymptotically periodic solutions for fractional integro-differential neutral equations

In this paper, we study the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of class r for fractional integro-differential neutral equations. An example is presented to illustrate the application of the abstract results.