With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it...With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.展开更多
Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the...Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x...By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.展开更多
In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
Abstrac In this paper, we discuss the existence of the solution and coupled minimal and maximal quasi-solutions for nonlinear non-monotone operator equation x = A(x, x), improved and generalized many relevant results.
In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved tha...In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.展开更多
文摘With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.
文摘Aim The existence of generalized solution for a class of nonlinear partial differential equations with nonhanogeneous boundary condition was investigated. This problem arises from polymer processing concerned with the first initial-boundary value problem or the nonstationary floW of non-Newtonian viscous incompressiblee fluid through the slit dice. MethodsThe monotone operator theory and the Schauder's fixal point theorem were used. Results and Conclusion The existence theorem of generalized solutions for a the of nonlinear partial differential equations with nonhormogeneous boundary condition is proved under reasonable conditions
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
基金Supported by the Scientific Research Foundation of Henan Provincial Education Com mittee(1999110018)
文摘By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.
文摘In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
文摘Abstrac In this paper, we discuss the existence of the solution and coupled minimal and maximal quasi-solutions for nonlinear non-monotone operator equation x = A(x, x), improved and generalized many relevant results.
文摘In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.
