Weak solutions of semilinear elliptic equation involving Dirac mass

  • Huyuan Chen

    Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
  • Patricio Felmer

    Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071, CNRS-UChile, Universidad de Chile, Chile
  • Jianfu Yang

    Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Abstract

In this paper, we study the elliptic problem with Dirac mass

where , , , is the Dirac mass at the origin and the potential is locally Lipchitz continuous in , with non-empty support and satisfying

with , and . We obtain two positive solutions of (1) with additional conditions for parameters on , and . The first solution is a minimal positive solution and the second solution is constructed via Mountain Pass Theorem.

Cite this article

Huyuan Chen, Patricio Felmer, Jianfu Yang, Weak solutions of semilinear elliptic equation involving Dirac mass. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 3, pp. 729–750

DOI 10.1016/J.ANIHPC.2017.08.001