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Nash equilibrium is the solution of this kind of game.
The solution of this kind of PDEs may encounter smooth transitions, or there can be large gradients of the field variables.
The numerical solution of this kind of problems can be obtained using the finite difference method and the finite element method (FEM) [1, 3, 4].
The solution of this kind of FBSDEs played an important role in the construction of optimal controls and Nash equilibrium points.
The aim of the numerical study is to implicitly device some guidelines to be used in the solution of this kind of problems.
The thickening effect in an aqueous solution of this kind of polymer depends on intermolecular hydrophobic associations and also on chain entanglements if the polymer concentration is significantly above the overlap concentration.
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By using the Yosida approximation technique for m-accretive operator, we prove some existence and uniqueness theorems of solutions for this kind of system of generalized variational inclusions.
A new system of generalized variational inclusions in the Banach space under the assumption with no continuousness is introduced, and some existence and uniqueness theorems of solutions for this kind of system of generalized variational inclusions are proved by using the Yosida approximation technique for m-accretive operator.
By using the resolvent operator due to Lan-Cho-Verma associated with -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative algorithm for this system of set-valued variational inclusions and an existence theorem of solutions for this kind of the variational inclusions system.
Then, applying the matrix analysis and the vector-valued mapping fixed point analysis method, an existence theorem of solutions for this kind of the system is established.
But solutions of this kind can only be arrived at with our own knowledge of our domestic set up.
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