This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x...This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.展开更多
In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions.
The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence th...The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite. number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.展开更多
The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain exist...In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .展开更多
文摘This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘In this paper, we investigate the asymptotic behavior of the extremal solutions of a difference equation and their character and prove the existence of the non-extremal solutions.
文摘The existence of solutions for systems of nonlinear impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces is studied. Some existence theorems of extremal solutions are obtained, which extend the related results for this class of equations on a finite interval with a finite. number of moments of impulse effect. The results are demonstrated by means of an example of an infinite systems for impulsive integral equations.
文摘The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
文摘In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .
基金Tianshan Youth Technology Talents Training Program(2017Q032)Doctoral Starting Funds of Xinjiang Institute of Engineering(2016xgy351812)Education Department of Xinjiang Uygur Autonomous Region(2017jyt012006)
