Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3

Abstract EN

We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3|∇u|2dx)Δu+u=k(x)f(u)+h(x), x∈R3, u∈H1(R3), u>0, x∈R3, where f is asymptotically linear with respect to t at infinity.

Under appropriate assumptions on k,f, and h, existence of two positive solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory.