Existence of solutions for Kirchhoff type problems with critical nonlinearity in R~3

摘要

In this paper, we consider the existence and multiplicity of solutions of Kirchhoff type problems with critical nonlinearity in R~3: -ε~2(a + b)∫_(R3) |?u|~2dx)Δu + V(x)u = K(x)|u|~4u + h(x, u), (t, x) ∈ R × R~3. Under suitable assumptions, we prove that this has at least one solution and for any m ∈ N, it has at least m pairs of solutions.