The Experts below are selected from a list of 19410 Experts worldwide ranked by ideXlab platform
Leandro S Tavares - One of the best experts on this subject based on the ideXlab platform.
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a hardy littlewood sobolev type inequality for variable exponents and applications to quasilinear choquard equations involving variable exponent
Mediterranean Journal of Mathematics, 2019Co-Authors: Claudianor O Alves, Leandro S TavaresAbstract:In this work, we have proved a Hardy–Littlewood–Sobolev inequality for variable exponents. After that, we use this inequality together with the variational method to establish the existence of solution for a class of Choquard equations involving the p(x)-Laplacian Operator.
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a sub supersolution method for a class of nonlocal problems involving the p x p x Laplacian Operator and applications
Acta Applicandae Mathematicae, 2018Co-Authors: Gelson Dos C G Santos, Giovany M Figueiredo, Leandro S TavaresAbstract:In the present paper, we study the existence of solutions for some nonlocal problems involving the $p(x)$ -Laplacian Operator. The approach is based on a new sub-supersolution method.
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a hardy littlewood sobolev type inequality for variable exponents and applications to quasilinear choquard equations involving variable exponent
arXiv: Analysis of PDEs, 2016Co-Authors: Claudianor O Alves, Leandro S TavaresAbstract:In this work, we have proved a version of the Hardy-Littlewood-Sobolev inequality for variable exponents. After we use the variational method to establish the existence of solution for a class of Choquard equations involving the $p(x)$-Laplacian Operator.
Claudianor O Alves - One of the best experts on this subject based on the ideXlab platform.
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a hardy littlewood sobolev type inequality for variable exponents and applications to quasilinear choquard equations involving variable exponent
Mediterranean Journal of Mathematics, 2019Co-Authors: Claudianor O Alves, Leandro S TavaresAbstract:In this work, we have proved a Hardy–Littlewood–Sobolev inequality for variable exponents. After that, we use this inequality together with the variational method to establish the existence of solution for a class of Choquard equations involving the p(x)-Laplacian Operator.
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a hardy littlewood sobolev type inequality for variable exponents and applications to quasilinear choquard equations involving variable exponent
arXiv: Analysis of PDEs, 2016Co-Authors: Claudianor O Alves, Leandro S TavaresAbstract:In this work, we have proved a version of the Hardy-Littlewood-Sobolev inequality for variable exponents. After we use the variational method to establish the existence of solution for a class of Choquard equations involving the $p(x)$-Laplacian Operator.
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multiplicity and concentration of solutions for a quasilinear choquard equation
Journal of Mathematical Physics, 2014Co-Authors: Claudianor O Alves, Minbo YangAbstract:In this paper, we study a quasilinear Choquard equation involving the p-Laplacian Operator and a potential function V. Under suitable assumptions on V and the nonlinearity, we prove the existence, multiplicity, and concentration of solutions for the equation by variational methods.
Anand Louis - One of the best experts on this subject based on the ideXlab platform.
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hypergraph markov Operators eigenvalues and approximation algorithms
Symposium on the Theory of Computing, 2015Co-Authors: Anand LouisAbstract:The celebrated Cheeger's Inequality [AM85,a86] establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency matrix (and other related matrices) of graphs. It has remained open to define a suitable spectral model for hypergraphs whose spectra can be used to estimate various combinatorial properties of the hypergraph. In this paper we introduce a new hypergraph Laplacian Operator generalizing the Laplacian matrix of graphs. Our Operator can be viewed as the gradient Operator applied to a certain natural quadratic form for hypergraphs. We show that various hypergraph parameters (for e.g. expansion, diameter, etc) can be bounded using this Operator's eigenvalues. We study the heat diffusion process associated with this Laplacian Operator, and bound its parameters in terms of its spectra. All our results are generalizations of the corresponding results for graphs. We show that there can be no linear Operator for hypergraphs whose spectra captures hypergraph expansion in a Cheeger-like manner. Our Laplacian Operator is non-linear, and thus computing its eigenvalues exactly is intractable. For any k, we give a polynomial time algorithm to compute an approximation to the kth smallest eigenvalue of the Operator. We show that this approximation factor is optimal under the SSE hypothesis (introduced by [RS10]) for constant values of k. Finally, using the factor preserving reduction from vertex expansion in graphs to hypergraph expansion, we show that all our results for hypergraphs extend to vertex expansion in graphs.
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hypergraph markov Operators eigenvalues and approximation algorithms
arXiv: Discrete Mathematics, 2014Co-Authors: Anand LouisAbstract:The celebrated Cheeger's Inequality \cite{am85,a86} establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency matrix (and other related matrices) of graphs. It has remained open to define a suitable spectral model for hypergraphs whose spectra can be used to estimate various combinatorial properties of the hypergraph. In this paper we introduce a new hypergraph Laplacian Operator (generalizing the Laplacian matrix of graphs)and study its spectra. We prove a Cheeger-type inequality for hypergraphs, relating the second smallest eigenvalue of this Operator to the expansion of the hypergraph. We bound other hypergraph expansion parameters via higher eigenvalues of this Operator. We give bounds on the diameter of the hypergraph as a function of the second smallest eigenvalue of the Laplacian Operator. The Markov process underlying the Laplacian Operator can be viewed as a dispersion process on the vertices of the hypergraph that might be of independent interest. We bound the {\em Mixing-time} of this process as a function of the second smallest eigenvalue of the Laplacian Operator. All these results are generalizations of the corresponding results for graphs. We show that there can be no linear Operator for hypergraphs whose spectra captures hypergraph expansion in a Cheeger-like manner. For any $k$, we give a polynomial time algorithm to compute an approximation to the $k^{th}$ smallest eigenvalue of the Operator. We show that this approximation factor is optimal under the SSE hypothesis (introduced by \cite{rs10}) for constant values of $k$. Finally, using the factor preserving reduction from vertex expansion in graphs to hypergraph expansion, we show that all our results for hypergraphs extend to vertex expansion in graphs.
Lishan Liu - One of the best experts on this subject based on the ideXlab platform.
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iterative analysis of the unique positive solution for a class of singular nonlinear boundary value problems involving two types of fractional derivatives with p Laplacian Operator
Complexity, 2019Co-Authors: Fang Wang, Lishan Liu, Yumei ZouAbstract:This article is concerned with a class of singular nonlinear fractional boundary value problems with p-Laplacian Operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary conditions and nonlocal infinite-point boundary conditions, and different fractional orders are involved in the boundary conditions and the nonlinear term, respectively. Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone Operator, an interesting result on the iterative sequence of the uniqueness of positive solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. And we obtain the dependence of solution upon parameter. Furthermore, two numerical examples are presented to illustrate the application of our main results.
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nontrivial weak solution for a schrodinger kirchhoff type system driven by a p_1 p_2 p 1 p 2 Laplacian Operator
Bulletin of The Iranian Mathematical Society, 2018Co-Authors: Lishan LiuAbstract:In this paper, we investigate the existence of nontrivial weak solution for a Schrodinger–Kirchhoff-type system driven by a $$(p_1,p_2)$$ -Laplacian Operator under appropriate hypotheses. The proofs are based on the variational methods.
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positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p Laplacian Operator
Boundary Value Problems, 2017Co-Authors: Xinan Hao, Lishan Liu, Huaqing Wang, Yujun CuiAbstract:In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian Operator. Under different combinations of superlinearity and sublinearity of the nonlinearities, various existence results for positive solutions are derived in terms of different values of parameters via the Guo-Krasnosel’skii fixed point theorem.
Xin Wang - One of the best experts on this subject based on the ideXlab platform.
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Laplacian Operator based edge detectors
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007Co-Authors: Xin WangAbstract:Laplacian Operator is a second derivative Operator often used in edge detection. Compared with the first derivative-based edge detectors such as Sobel Operator, the Laplacian Operator may yield better results in edge localization. Unfortunately, the Laplacian Operator is very sensitive to noise. In this paper, based on the Laplacian Operator, a model is introduced for making some edge detectors. Also, the optimal threshold is introduced for obtaining a maximum a posteriori (MAP) estimate of edges
