Existence and Nonexistence of Positive Solutions for a Kirchhoff-type Equation with Inhomogeneous Strong Allee Effect

Abstract

In this paper, we deal with the nonlocal semilinear elliptic equation with inhomogeneous strong Allee effect  where the nonlocal coefficient  is a continuous function. By means of variational approach, we prove that the equation has at least two positive solutions for large λ under suitable hypotheses about nonlinearity. We also prove some nonexistence results. In particular, we shall give a positive answer to the conjecture by Liu, Wang and Shi’s of  [1].