The Experts below are selected from a list of 1695 Experts worldwide ranked by ideXlab platform
D. C. De Morais Filho - One of the best experts on this subject based on the ideXlab platform.
-
An Ambrosetti-Prodi-type problem for an elliptic system of equations via monotone iteration method and Leray-Schauder Degree theory
Abstract and Applied Analysis, 1996Co-Authors: D. C. De Morais FilhoAbstract:In this paper we employ the Monotone Iteration Method and the Leray-Schauder Degree Theory to study an ℝ2-parametrized system of elliptic equations. We obtain a curve dividing the plane into two regions. Depending on which region the parameter is, the system will or will not have solutions. This is an Ambrosetti-Prodi-type problem for a system of equations.
Xiyou Cheng - One of the best experts on this subject based on the ideXlab platform.
-
Positive solutions for a class of multi-parameter elliptic systems
Nonlinear Analysis: Real World Applications, 2013Co-Authors: Xiyou Cheng, Zhitao ZhangAbstract:Abstract In this paper, we deal with the global existence of positive solutions for a multi-parameter system of second-order elliptic equations with respect to parameters, by using the fixed point index theory in cones, the sub-supersolutions method, Leray–Schauder Degree theory and a priori estimates technique. In addition, for the computation of Leray–Schauder Degree on the Cartesian product of two ordered intervals, we also establish a result about Leray–Schauder Degree on a strict ordered interval induced by a pair of strict lower and upper solutions for a system of second-order elliptic equations.
-
A multiplicity result of positive solutions for a class of multi-parameter ordinary differential systems
Acta Mathematicae Applicatae Sinica English Series, 2012Co-Authors: Xiyou Cheng, Xiao-lin YanAbstract:In this paper, we establish a result of Leray-Schauder Degree on the order interval which is induced by a pair of strict lower and upper solutions for a system of second-order ordinary differential equations. As applications, we prove the global existence of positive solutions for a multi-parameter system of second-order ordinary differential equations with respect to parameters. The discussion is based on the result of Leray-Schauder Degree on the order interval and the fixed point index theory in cones.
-
Multiplicity of positive solutions for a (p"1,p"2)-Laplacian system and its applications
Nonlinear Analysis: Real World Applications, 2012Co-Authors: Xiyou ChengAbstract:Abstract In this paper, we establish the product formula for the fixed point index on product cone, and the relation between Leray–Schauder Degree and a pair of strict lower and upper solutions for a ( p 1 , p 2 ) -Laplacian system. Based on the product formula of the fixed point index and Leray–Schauder Degree theory, we deal with the multiplicity of positive solutions for a class of ( p 1 , p 2 ) -Laplacian systems. As applications, we prove the global existence of positive solutions for a multi-parameter system of ( p 1 , p 2 ) -Laplacian equations with respect to parameters.
Robert F Brown - One of the best experts on this subject based on the ideXlab platform.
-
Properties of the Leray–Schauder Degree
A Topological Introduction to Nonlinear Analysis, 2014Co-Authors: Robert F BrownAbstract:You may have noticed that once the Brouwer Degree was defined and its properties established, we used it in the chapter that followed only in a sort of formal way. In defining the Leray-Schauder Degree we needed to know that there was a well-defined integer, called the Brouwer Degree, represented by the symbol d(I∈ - f∈, U∈), but we did not have to specify how that integer was defined. Furthermore, and this is the point I want to emphasize, in the proof that the Leray-Schauder Degree is well-defined, which is really a theorem about the Brouwer Degree, all we needed to know about that Degree was two of its properties: homotopy and reduction of dimension. In this chapter, I will list and demonstrate properties of the Leray-Schauder Degree; properties which, basically, are consequences of the corresponding properties of the Brouwer Degree. Again all we will need to know about the Brouwer Degree is its existence and properties. As in the previous chapter, no homology groups will ever appear. Then, once we have established these properties of the Leray-Schauder Degree, that’s all we’ll need to know about that Degree for the rest of the book. In other words, after this chapter we can forget how the Degree was defined.
-
Properties of the Leray-Schauder Degree
A Topological Introduction to Nonlinear Analysis, 2014Co-Authors: Robert F BrownAbstract:You may have noticed that once the Brouwer Degree was defined and its properties established, we used it in the chapter that followed only in a sort of formal way. In defining the Leray-Schauder Degree we needed to know that there was a well-defined integer, called the Brouwer Degree, represented by the symbol d(I∈ - f∈, U∈), but we did not have to specify how that integer was defined. Furthermore, and this is the point I want to emphasize, in the proof that the Leray-Schauder Degree is well-defined, which is really a theorem about the Brouwer Degree, all we needed to know about that Degree was two of its properties: homotopy and reduction of dimension. In this chapter, I will list and demonstrate properties of the Leray-Schauder Degree; properties which, basically, are consequences of the corresponding properties of the Brouwer Degree. Again all we will need to know about the Brouwer Degree is its existence and properties. As in the previous chapter, no homology groups will ever appear. Then, once we have established these properties of the Leray-Schauder Degree, that’s all we’ll need to know about that Degree for the rest of the book. In other words, after this chapter we can forget how the Degree was defined.
-
Leray-Schauder Degree
A Topological Introduction to Nonlinear Analysis, 2014Co-Authors: Robert F BrownAbstract:The objective of Leray-Schauder Degree theory is the same as that of the fixed point theory of the first part of the book. We want to demonstrate that if certain hypotheses are satisfied, then we can conclude that a map f has a fixed point, that is, that f(x) = x. If the hypotheses are of the right type, we can hope to verify them in settings that arise in analysis and conclude that an analytic problem has a solution because we’ve managed to describe its solutions as fixed points. A major difference between Leray-Schauder theory and what we studied previously is the local nature of our new theory. A fixed point theorem generally states the existence of a fixed point somewhere in the domain of a map defined on an entire space. Degree theory, as in the last chapter, is concerned with a map defined on \( \bar U \), the closure of a specified open set U. Leray-Schauder theory seeks conditions that imply the map has a fixed point specifically on U.
-
The Fixed Point Index
A Topological Introduction to Nonlinear Analysis, 2014Co-Authors: Robert F BrownAbstract:We have used the Leray–Schauder Degree to find fixed points of a map from an open subset of a normed linear space to that space. That was the setting of the forced pendulum problem of Part II and we will return to it for the bifurcation theory of Part IV. But there are many interesting problems for which we cannot use the entire normed linear space, but instead their formulation leads us to a map of a closed convex subset of a normed linear space that is not a linear subspace. There is a generalization of the Leray–Schauder Degree, called the fixed point index, that is, designed to find fixed points of such a map. Our goal in this chapter is to define the index and list its properties. Then, in the subsequent chapters of this part, I will show you some ways in which this tool is used.
-
The Degree Calculation
A Topological Introduction to Nonlinear Analysis, 2004Co-Authors: Robert F BrownAbstract:In this chapter, we will use the spectrum of a compact linear operator to establish an important fact about the Leray-Schauder Degree. As in the previous chapter, X is an infinite-dimensional Banach space.
Vv Motreanu - One of the best experts on this subject based on the ideXlab platform.
-
On the study of a class of variational inequalities via Leray-Schauder Degree
Fixed Point Theory and Applications, 2004Co-Authors: D Goeleven, D Motreanu, Vv MotreanuAbstract:We present existence results for general variational inequalities without monotonicity or coercivity assumptions. It relies on a Leray-Schauder Degree approach and provides additional information about the location of solutions.
D Goeleven - One of the best experts on this subject based on the ideXlab platform.
-
On the study of a class of variational inequalities via Leray-Schauder Degree
Fixed Point Theory and Applications, 2004Co-Authors: D Goeleven, D Motreanu, Vv MotreanuAbstract:We present existence results for general variational inequalities without monotonicity or coercivity assumptions. It relies on a Leray-Schauder Degree approach and provides additional information about the location of solutions.
