In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscil...In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.展开更多
1 Introduction Alkaline lakes are widely distributed in the area of the Qinghai-Tibet Plateau.Most of the salt lakes are famous for their high concentration of lithium,potassium,magnesium,boron(Ma,2000).In recent year...1 Introduction Alkaline lakes are widely distributed in the area of the Qinghai-Tibet Plateau.Most of the salt lakes are famous for their high concentration of lithium,potassium,magnesium,boron(Ma,2000).In recent years,as a new energy material,lithium and its compounds are widely used in the new area,such as aerospace industry,nuclear展开更多
The existence of monotone and non_monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector...The existence of monotone and non_monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi_symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi_stable, the existence of infinitely many monotone solusion is obtained.展开更多
In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also ex...In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.展开更多
The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the syst...The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the system has a unique limit cycle, homoclinic orbits, canards or the unique equilibrium point is globally asymptotic stable are given. The methods in our previous papers are used for the proofs.展开更多
Fundamental physical and (electro) chemical principles of rechargeable battery operation form the basis of the electronic network models developed for Nickel-based aqueous battery systems, including Nickel Metal Hydri...Fundamental physical and (electro) chemical principles of rechargeable battery operation form the basis of the electronic network models developed for Nickel-based aqueous battery systems, including Nickel Metal Hydride (NiMH), and non-aqueous battery systems, such as the well-known Li-ion. Refined equivalent network circuits for both systems represent the main contribution of this paper. These electronic network models describe the behavior of batteries during normal operation and during over (dis) charging in the case of the aqueous battery systems. This makes it possible to visualize the various reaction pathways, including convention and pulse (dis) charge behavior and for example, the self-discharge performance.展开更多
文摘In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.
基金Financial support from the NSFCs (21106103, 21276194 and 21306136)the Specialized Research Funds for the Doctoral Program of Chinese Higher Education (20101208110003 and 20111208120003)+1 种基金the Natural Science Foundation of Tianjin (12JCQNJC03400)the Senior Professor Program for TUST (20100405)
文摘1 Introduction Alkaline lakes are widely distributed in the area of the Qinghai-Tibet Plateau.Most of the salt lakes are famous for their high concentration of lithium,potassium,magnesium,boron(Ma,2000).In recent years,as a new energy material,lithium and its compounds are widely used in the new area,such as aerospace industry,nuclear
文摘The existence of monotone and non_monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi_symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi_stable, the existence of infinitely many monotone solusion is obtained.
文摘In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.
文摘The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the system has a unique limit cycle, homoclinic orbits, canards or the unique equilibrium point is globally asymptotic stable are given. The methods in our previous papers are used for the proofs.
文摘Fundamental physical and (electro) chemical principles of rechargeable battery operation form the basis of the electronic network models developed for Nickel-based aqueous battery systems, including Nickel Metal Hydride (NiMH), and non-aqueous battery systems, such as the well-known Li-ion. Refined equivalent network circuits for both systems represent the main contribution of this paper. These electronic network models describe the behavior of batteries during normal operation and during over (dis) charging in the case of the aqueous battery systems. This makes it possible to visualize the various reaction pathways, including convention and pulse (dis) charge behavior and for example, the self-discharge performance.
