Multiplicity of single-bump solutions for semilinear elliptic equations in multi-bump domains Original Research Article

In this paper, we study the decomposition of the filtration of the Nehari manifold via the variation of domain shape. Furthermore, we use this result to prove that the semilinear elliptic equation in the multi-bump domain Ω(r)Ω(r) has multiple positive solutions and we can find at least one ground state solution.