This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemiv...This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.展开更多
In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differe...In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differential inclusions, we devise a Lyapunov stability theorem suitable for this class of switched systems. With this, we prove a Lyapunov stability theorem for piecewise linear switched systems by means of a concrete class of Lyapunov functions. Contrary to existing results on the subject, the stability theorems in this paper include Filippov （or relaxed） solutions and allow infinite switching in finite time. Finally, we show that for a class of piecewise linear switched systems, the inertia of the system is not sufficient to determine its stability. A number of examples are provided to illustrate the concepts discussed in this paper.展开更多
The present paper is concerned with botmdary value problem.for differential inclusions of second order in separable Banach spaces,an existence resuh is proved under weaker conditions and some existence theorems.for no...The present paper is concerned with botmdary value problem.for differential inclusions of second order in separable Banach spaces,an existence resuh is proved under weaker conditions and some existence theorems.for nonlinear second order systems can be deduced.form this paper stheorems.展开更多
In this paper a fixed point theorem for contracting maps is used to investigate the existence of solutions to a class of higher-order differential inclusions with (k, n-k) conjugate multi-point boundary value problem.
We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions an...We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.展开更多
基金This research is supported by the National Natural Science Foundation of China(10171008)
文摘This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.
基金supported by the Danish Council for Technology and Innovation
文摘In this paper, we formulate a uniform mathematical framework for studying switched systems with piecewise linear partitioned state space and state dependent switching. Based on known results from the theory of differential inclusions, we devise a Lyapunov stability theorem suitable for this class of switched systems. With this, we prove a Lyapunov stability theorem for piecewise linear switched systems by means of a concrete class of Lyapunov functions. Contrary to existing results on the subject, the stability theorems in this paper include Filippov （or relaxed） solutions and allow infinite switching in finite time. Finally, we show that for a class of piecewise linear switched systems, the inertia of the system is not sufficient to determine its stability. A number of examples are provided to illustrate the concepts discussed in this paper.
文摘The present paper is concerned with botmdary value problem.for differential inclusions of second order in separable Banach spaces,an existence resuh is proved under weaker conditions and some existence theorems.for nonlinear second order systems can be deduced.form this paper stheorems.
基金supported by the National Natural Science Foundation of China (10971179)
文摘In this paper a fixed point theorem for contracting maps is used to investigate the existence of solutions to a class of higher-order differential inclusions with (k, n-k) conjugate multi-point boundary value problem.
文摘We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.
