On the Dirichlet problem involving non-linearities with non-positive primitive: a problem and a remark

Abstract

In this article, we consider the Dirichlet problem for a semilinear elliptic equation involving a non-linearity with non-positive primitive. We propose an open problem and give a partial answer to it.

Keywords:

• Dirichlet problem
• semilinear elliptic equation
• Pohozaev identity
• non-linearity with non-positive primitive

AMS Subject Classifications::

• 35J60
• 35P15
• 35P30

Acknowledgement

The research of X. Fan has been supported by the National Natural Science Foundation of China (10671084).