Classification of Solutions for a System of Integral Equations

By Wenxiong CHEN *, Congming LI #, B. Ou. 2005

251 citations recorded by the source corpus.

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In Applied Mathematics

Citations in the corpus

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems (2008, methodology): “2) and the integrability condition (u, v) ∈ L(R )×L(R ), solutions of this problem are rescaled optimizers of the well known Hardy-LittlewoodSobolev inequality (see for instance [3, 4, 13, 14]), ∣∣∣∣ ∫ RN ∫”
Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy–Littlewood–Sobolev system of integral equations (2012, background): “9 and the corresponding partial differential equations have been studied extensively in the last 40 years, see more details in [2,3,5–11,13–22].”
A Liouville type Theorem for an integral system (2006, methodology): “We shall use Chen-Li-Ou’s method [3] [4] to prove this theorem.”
Liouville type theorems for integral equations and integral systems (2013, unknown): “By the results of [9] and [10] we know that u = a ( t t2+|x−x0|2 ) N−α 2 and v = b ( t t2+|x−x0|2 ) N−α 2 .”
CLASSIFICATION OF POSITIVE SOLUTIONS FOR NONLINEAR DIFFERENTIAL AND INTEGRAL SYSTEMS WITH CRITICAL EXPONENTS (2009, result): “Our results, as well as the results of [16] and [23], are motivated by the previous work [7], where Chen, Li, and Ou considered the integral system:”
Liouville Type Theorems for PDE and IE Systems Involving Fractional Laplacian on a Half Space (2017, methodology): “In [9], the authors developed the method of moving planes of [15, 16] in integral forms and proved under global integrability conditions that in the critical cases every positive entire solutions (u, v) to a IE system involving fractional Laplacian are radially symmetric and monotonic decreasing abo”
Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, methodology): “There are many more applications of this method to integral systems, and the interested readers may see [10] [12] [15] [20] [21] [28] [33] [34] [40] [42] [45] [46] [47] [50] [53] [54] and the references therein.”
Radial symmetry and monotonicity for an integral equation (2008, methodology): “Recently, it was first observed by Chen, Li and Ou [4,5,12] that instead of the maximum principle, one can use a Hardy–Littlewood–Sobolev (HLS) type inequality to obtain the radial symmetry and monotonicity of nonnegative solutions of (systems of) elliptic equations of Yamabe type.”
Regularity of solutions for an integral system of Wolff type (2011, background): “Then the radial symmetry for solutions of system (12) in critical case was obtained in [12]:”
Classification of Positive Solitary Solutions of the Nonlinear Choquard Equation (2010, methodology): “In this section, we prove Theorem 2 using the method of moving plane in integral form, which was introduced by Chen et al. [5, 6 ].”
Quantitative analysis of some system of integral equations (2006, background): “Furthermore, another paper from Chen, Li an Ou [ 11 ] discussed the Euler-”