On nonlocal nonlinear elliptic problem with the fractional Laplacian

2014/12/31 by Li Ma, Ma, Li · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1501.00070

Abstract

In this paper, we study a nonlocal elliptic problem with the fractional Laplacian on Rⁿ. We show that the problem has infinite positive solutions in C^τ(Rⁿ)\bigcap H^α_loc(Rⁿ). Moreover each of these solutions tends to some positive constant limit at infinity. We extend Lin's result to the nonlocal problem on Rⁿ.

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