The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Zengqin Zhao - One of the best experts on this subject based on the ideXlab platform.
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Sign-changing solution for a third-order boundary-value problem in Ordered Banach Space with lattice structure
Boundary Value Problems, 2014Co-Authors: Zengqin ZhaoAbstract:In this paper, the sign-changing solution of a third-order two-point boundary-value problem is considered. By calculating the eigenvalues and the algebraic multiplicity of the linear problem and using a new fixed point theorem in an Ordered Banach Space with lattice structure, we give some conditions to guarantee the existence for a sign-changing solution.
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Positive Fixed Points for Semipositone Operators in Ordered Banach Spaces and Applications
Abstract and Applied Analysis, 2013Co-Authors: Zengqin ZhaoAbstract:The theory of semipositone integral equations and semipositone ordinary differential equations has been emerging as an important area of investigation in recent years, but the research on semipositone operators in abstract Spaces is yet rare. By employing a well-known fixed point index theorem and combining it with a translation substitution, we study the existence of positive fixed points for a semipositone operator in Ordered Banach Space. Lastly, we apply the results to Hammerstein integral equations of polynomial type.
Pengyu Chen - One of the best experts on this subject based on the ideXlab platform.
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Positive solutions for periodic boundary value problem of fractional differential equation in Banach Spaces
SpringerOpen, 2018Co-Authors: Yibo Kong, Pengyu ChenAbstract:Abstract This paper discusses the existence and uniqueness of positive solutions for a periodic boundary value problem of a fractional differential equation in an Ordered Banach Space E. The existence and uniqueness results of solutions for the associated linear periodic boundary value problem of the fractional differential equation are established, and the norm estimation of resolvent operator is accurately obtained. With the aid of this estimation, the existence and uniqueness results of positive solutions are obtained by using a monotone iterative technique
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monotone iterative technique for a class of semilinear evolution equations with nonlocal conditions
Results in Mathematics, 2013Co-Authors: Pengyu ChenAbstract:This paper discusses the existence and uniqueness of mild solutions for a class of semilinear evolution equations with nonlocal conditions in an Ordered Banach Space E. Under some monotonicity conditions and noncompactness measure conditions of the nonlinearity, a new monotone iterative method on the evolution equations with nonlocal conditions has been established. Particularly, an existence result without using noncompactness measure condition is obtained in Ordered and weakly sequentially complete Banach Spaces, which is very convenient for application. An example to illustrate our main results is also given.
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mixed monotone iterative technique for a class of semilinear impulsive evolution equations in Banach Spaces
Nonlinear Analysis-theory Methods & Applications, 2011Co-Authors: Pengyu ChenAbstract:Abstract This paper deals with the existence of mild L -quasi-solutions to the initial value problem for a class of semilinear impulsive evolution equations in an Ordered Banach Space E . Under a new concept of upper and lower solutions, a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established. The results improve and extend some relevant results in ordinary differential equations and partial differential equations. An example is also given.
Ravi P. Agarwal - One of the best experts on this subject based on the ideXlab platform.
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fixed point theorems via mnc in Ordered Banach Space with application to fractional integro differential evolution equations
Taiwanese Journal of Mathematics, 2017Co-Authors: Hemant Kumar Nashine, He Yang, Ravi P. AgarwalAbstract:In this paper, we propose fixed point results through the notion of measure of noncompactness (MNC) in partially Ordered Banach Spaces. We also prove some new coupled fixed point results via MNC for more general class of function. To achieve this result, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. Further, we apply the obtained fixed point theorems to prove the existence of mild solutions for fractional integro-differential evolution equations with nonlocal conditions. At the end, an example is given to illustrate the rationality of the abstract results for fractional parabolic equations.
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fixed point theorems in Ordered Banach Spaces and applications to nonlinear integral equations
Abstract and Applied Analysis, 2012Co-Authors: Ravi P. Agarwal, Nawab Hussain, Mohamedaziz TaoudiAbstract:We present some new common fixed point theorems for a pair of nonlinear mappings defined on an Ordered Banach Space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.
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Common fixed point theorems for a pair of countably condensing mappings in Ordered Banach Spaces
Journal of Applied Mathematics and Stochastic Analysis, 2003Co-Authors: Bapurao C Dhage, Donal O'regan, Ravi P. AgarwalAbstract:In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an Ordered Banach Space are proved.
He Yang - One of the best experts on this subject based on the ideXlab platform.
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fixed point theorems via mnc in Ordered Banach Space with application to fractional integro differential evolution equations
Taiwanese Journal of Mathematics, 2017Co-Authors: Hemant Kumar Nashine, He Yang, Ravi P. AgarwalAbstract:In this paper, we propose fixed point results through the notion of measure of noncompactness (MNC) in partially Ordered Banach Spaces. We also prove some new coupled fixed point results via MNC for more general class of function. To achieve this result, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. Further, we apply the obtained fixed point theorems to prove the existence of mild solutions for fractional integro-differential evolution equations with nonlocal conditions. At the end, an example is given to illustrate the rationality of the abstract results for fractional parabolic equations.
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Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces
Abstract and Applied Analysis, 2010Co-Authors: He YangAbstract:This paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an Ordered Banach Space E:u′(t)
Xuemei Zhang - One of the best experts on this subject based on the ideXlab platform.
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Positive Fixed Point of Strict Set Contraction Operators on Ordered Banach Spaces and Applications
Abstract and Applied Analysis, 2010Co-Authors: Meiqiang Feng, Xuemei ZhangAbstract:The fixed point theorem of cone expansion and compression of norm type for a strict set contraction operator is generalized by replacing the norms with a convex functional satisfying certain conditions. We then show how to apply our theorem to prove the existence of a positive solution to a second-order differential equation with integral boundary conditions in an Ordered Banach Space. An example is worked out to demonstrate the main results.