Classification of solutions for an integral equation

By Wenxiong CHEN *, Congming LI #, B. Ou. 2006

989 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0254c441ff9689ced302c10a6212f3b1f31b6004

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Uniqueness of non-linear ground states for fractional Laplacians in $${\mathbb{R}}$$R (2010, background): “• Optimizers for fractional Sobolev inequalities in d > 1 dimensions; see [12, 21].”
Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, methodology): “For instance, in [19], we showed that (3) is equivalent to semi-linear elliptic PDE (4) and thus classified all the positive solutions for both integral equation (3) and PDE (4).”
Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian (2015, methodology): “It is a direct consequence of Theorem 1 and the following results from [11] and [12]: Proposition 2.”
Semilinear fractional elliptic equations involving measures (2013, background): “Recently, great attention has been devoted to non-linear equations involving fractional Laplacian or more general integro-differential operators and we mention the reference [8, 9, 10, 14, 15, 24, 30, 32].”
A concave—convex elliptic problem involving the fractional Laplacian (2010, background): “As to the concave-convex nonlinearity, there is a huge amount of results involving different (local) operators, see for instance [1, 4, 8, 17, 19, 24].”
Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (2019, methodology): “It has been proved by Chen-Li-Ou [12] that every smooth positive solution u of (10) with a nonremovable singularity at the origin is radially symmetric.”
Liouville Type Theorems for PDE and IE Systems Involving Fractional Laplacian on a Half Space (2017, methodology): “In this paper, we will study the non-existence of nontrivial nonnegative locally integrable solutions of the IE system (4) by using the method of moving planes [15, 16] (see also [3, 6, 20, 23]) in integral forms initially used in [8, 9].”
Sharp criteria of Liouville type for some nonlinear systems (2013, background): “The equivalence between integral equations (IEs) and PDEs was studied in [9] and [12], which provides a technique in studying the PDEs: one can use the corresponding integral equations to investigate the global properties for those solutions.”
On finite Morse index solutions of higher order fractional Lane-Emden equations (2014, result): “For the case of 0 s 1, a counterpart of the classification results of Gidas-Spruck [12] and CaffarelliGidas-Spruck [1] holds for the fractional Lane-Emden equation, see the work of Li [14] and Chen-Li-Ou [5].”